Free Printable Quadratics and Factoring Practice

1.

Which of the following is Standard Form?

a)

$y=ax^2+bx+c$

b)

$y=a\left(x-p\right)\left(x-q\right)$

c)

$y=a\left(x-h\right)^2+k$

2.

Which of the following is Vertex Form?

a)

$y=ax^2+bx+c$

b)

$y=a\left(x-p\right)\left(x-q\right)$

c)

$y=a\left(x-h\right)^2+k$

3.

Which of the following is Factored Form?

a)

$y=ax^2+bx+c$

b)

$y=a\left(x-p\right)\left(x-q\right)$

c)

$y=a\left(x-h\right)^2+k$

4.

Convert to Vertex Form:

f(x) = x² +8x +14

a)

f(x) = (x - 4)² + 2

b)

f(x) = (x - 4)² - 2

c)

f(x) = (x + 4)² + 2

d)

f(x) = (x + 4)² - 2

5.

Convert to standard form:

f(x) = x²+3x-18

a)

(x-6)(x+3)

b)

(x+6)(x+3)

c)

(x+6)(x-3)

d)

(x-6)(x-3)

6.

Convert to Standard Form:

f(x) = (x+7)(x-3)

a)

f(x) = x² +10x +21

b)

f(x) = x² -10x -21

c)

f(x) = x² +4x -21

d)

f(x) = x² +4x +21

7.

Convert to standard form: $y=\left(x+5\right)^2-15$

a)

$y=x^2+10$

b)

$y=x^2+10x\ +10$

c)

$y=x^2+25$

d)

$y=x^2+10x+25$

8.

Convert to standard form: $y=-2\left(x-3\right)^2+6$

a)

$y=-2x^2+12x-12$

b)

$y=-2x^2+6x+15$

c)

$y=-2x^2+12x-18$

d)

$y\ =\ -2x^2-12$

9.

Convert to Factored Form:

3a² + 4a + 1

a)

(7a-10)(a-8)

b)

Not factorable

c)

(3a+1)(a+1)

d)

(3a-1)(a-1)

10.

Convert to Factored Form:

x² - 10x + 24

a)

(x - 6)(x - 4)

b)

(x + 6)(x + 4)

c)

(x - 12)(x + 2)

d)

(x - 8)(x - 3)

11.

Determine the vertex of the parabola y=5(x-2)²–7

a)

(5, -7)

b)

(-2, -7)

c)

(2, -7)

d)

(-7, -2)

12.

What is the y-intercept of
f(x)=2x² + 4x + 6

a)

(6 , 0)

b)

(-6 , 0)

c)

(0, -6)

d)

(0 , 6)

13.

What are the x-intercepts for the function?

f(x) = (x + 7)(x + 5)

a)

(7 , 0) and (5 , 0)

b)

(0 , 7) and (0 , 5)

c)

(-7 , 0) and (-5 , 0)

d)

(7 , 0) and (5 , 0)

14.

What is the vertex form of this quadratic?

a)

f(x) = -(x + 2)²- 4

b)

f(x) = (x - 2)²+ 4

c)

f(x) = (x - 2)²- 4

d)

f(x) = -(x - 2)² - 4

15.

Which of the following is Standard Form?

a)

$y=ax^2+bx+c$

b)

$y=a\left(x-p\right)\left(x-q\right)$

c)

$y=a\left(x-h\right)^2+k$

16.

Which of the following is Vertex Form?

a)

$y=ax^2+bx+c$

b)

$y=a\left(x-p\right)\left(x-q\right)$

c)

$y=a\left(x-h\right)^2+k$

17.

What is an equation of a parabola with the vertex of $\left(3,-4\right)$ ?

a)

$y=-\frac{1}{2}\left(x+3\right)^2-4$

b)

$y=2\left(x-3\right)^2+4$

c)

$y=\frac{3}{2}\left(x-3\right)^2-4$

d)

$y=\left(x+3\right)^2+4$

18.

What is an equation of a parabola with the vertex of $\left(-2,-4\right)$ ?

a)

$y=-\left(x+2\right)^2-4$

b)

$y=\frac{3}{2}\left(x-2\right)^2+4$

c)

$y=\frac{3}{2}\left(x-2\right)^2-4$

d)

$y=\left(x+2\right)^2+4$

19.

What is an equation of a parabola with the vertex of $\left(4,9\right)$ ?

a)

$y=-\frac{4}{5}\left(x+4\right)^2-9$

b)

$y=\frac{3}{4}\left(x-4\right)^2+9$

c)

$y=-\frac{5}{2}\left(x-4\right)^2-9$

d)

$y=\left(x+4\right)^2+9$

20.

Which of the following is Intercept (Factored) Form?

a)

$y=ax^2+bx+c$

b)

$y=a\left(x-p\right)\left(x-q\right)$

c)

$y=a\left(x-h\right)^2+k$

21.

What is an equation of a quadratic with x-intercepts at $\left(-1,0\right)$ and $\left(-10,0\right)$

a)

$y=-2\left(x+1\right)\left(x-10\right)$

b)

$y=\frac{1}{3}\left(x+1\right)\left(x+10\right)$

c)

$y=-\frac{1}{10}\left(x-1\right)\left(x+10\right)$

d)

$y=3\left(x-1\right)\left(x-10\right)$

22.

What is an equation of a quadratic with x-intercepts at $\left(4,0\right)$ and $\left(-5,0\right)$

a)

$y=-\frac{1}{3}\left(x+4\right)\left(x-5\right)$

b)

$y=4\left(x+4\right)\left(x+5\right)$

c)

$y=-\frac{4}{5}\left(x-4\right)\left(x+5\right)$

d)

$y=3\left(x-4\right)\left(x-5\right)$

23.

What is an equation of a quadratic with x-intercepts at $\left(7,0\right)$ and $\left(11,0\right)$

a)

$y=-\frac{1}{3}\left(x+7\right)\left(x-11\right)$

b)

$y=-\left(x+7\right)\left(x+11\right)$

c)

$y=\frac{2}{5}\left(x-7\right)\left(x+11\right)$

d)

$y=\frac{3}{2}\left(x-7\right)\left(x-11\right)$

24.

$y=-\frac{2}{3}\left(x-4\right)^2+10$ What is the vertex of the parabola with the equation

a)

$\left(4,10\right)$

b)

$\left(-4,10\right)$

c)

$\left(4,-10\right)$

d)

$\left(-4,-10\right)$

25.

$y=5\left(x+3\right)^2-2$ What is the vertex of the parabola with the equation

a)

$\left(3,2\right)$

b)

$\left(-3,2\right)$

c)

$\left(3,-2\right)$

d)

$\left(-3,-2\right)$

26.

$y=-\frac{5}{3}\left(x-1\right)^2$ What is the vertex of the parabola with the equation

a)

$\left(1,0\right)$

b)

$\left(-1,0\right)$

27.

$y=8\left(x-2\right)\left(x+3\right)$ What are the zeros (x-intercepts) of the equation

a)

$\left(2,0\right)\ and\ \left(3,0\right)$

b)

$\left(-2,0\right)\ and\ \left(3,0\right)$

c)

$\left(2,0\right)\ and\ \left(-3,0\right)$

d)

$\left(-2,0\right)\ and\ \left(-3,0\right)$

28.

$y=-\frac{2}{3}\left(x+1\right)\left(x+3\right)$ What are the zeros (x-intercepts) of the equation

a)

$\left(1,0\right)\ and\ \left(3,0\right)$

b)

$\left(-1,0\right)\ and\ \left(3,0\right)$

c)

$\left(1,0\right)\ and\ \left(-3,0\right)$

d)

$\left(-1,0\right)\ and\ \left(-3,0\right)$

29.

$y=\frac{1}{4}\left(x+5\right)\left(x-6\right)$ What are the zeros (x-intercepts) of the equation

a)

$\left(5,0\right)\ and\ \left(6,0\right)$

b)

$\left(-5,0\right)\ and\ \left(6,0\right)$

c)

$\left(5,0\right)\ and\ \left(-6,0\right)$

d)

$\left(-5,0\right)\ and\ \left(-6,0\right)$

30.

What do we call the graph of a quadratic function?

a)

parabola

b)

linear

c)

cubic

d)

sinusoidal

31.

Which of the following is an example of a quadratic function?

a)

b)

c)

d)

32.

Which of the following equations matches vertex form of a quadratic?

a)

y = a(x + h)² - k

b)

y = a(x - h)² + k

c)

y = ax² + bx + c

d)

y = mx + b

33.

Which of the following equations matches standard form of a quadratic?

a)

ax + by = c

b)

y = a(x - h)² + k

c)

y = ax² + bx + c

d)

y = mx + b

34.

What is the "formula" for finding the axis of symmetry?

a)

$y=ax^2+bx+c$

b)

$x=\frac{-b}{2a}$

c)

$y=mx+b$

d)

$x=\frac{-b\pm\sqrt{b^2-4ac}}{2a}$

35.

Define X-intercept

a)

The highest or lowest point on the graph

b)

Where the parabola touches or intersects the x-axis

c)

Where the parabola touches or intersects the y-axis

d)

A line that divides the graph into two equal parts. i.e. cuts the graph in half

36.

What are the x-intercepts on the graph?

Check all that apply.

a)

$\left(0,\ -3\right)$

b)

$\left(1,\ -4\right)$

c)

$\left(-1,\ 0\right)$

d)

$\left(3,\ 0\right)$

e)

$\left(1,\ 0\right)$

37.

Define Y-intercept

a)

Where the parabola touches or intersects the x-axis, also called the x-intercept

b)

The lowest y-value on the graph

c)

The highest y-value on the graph

d)

Where the parabola touches or intersects the y-axis

38.

If "a" is negative, does the parabola open up or down? Does it have a maximum or minimum?

a)

Down, Max

b)

Down, Min

c)

Up, Max

d)

Up, Min

39.

When a parabola opens downward the vertex is

a)

a minimum

b)

a maximum

c)

a vertex

d)

a parabola

40.

What is the significance of the ordered pair (2, -4) to the graph?

a)

It is the vertex

b)

It is an x-intercept

c)

It is the y-intercept

d)

It is the axis of symmetry

41.

The axis of symmetry line passes through which point?

a)

y-intercept

b)

any random point

c)

vertex

d)

x-intercept

42.

A parabola has a vertex at (5, -3).

Where is the axis of symmetry?

a)

y = -3

b)

x = -3

c)

x = 5

d)

(5, -3)

43.

Use the graph to determine the solutions.

(Hint: locate the x-intercepts)

a)

-1 and -3

b)

1 and -3

c)

1 and 3

d)

- 4

44.

What is the y-intercept of this graph?

a)

It is the vertex

b)

(0, -2)

c)

(5, 0)

d)

( -1, 0)

45.

The axis of symmetry line passes through which point?

a)

y-intercept

b)

any random point

c)

vertex

d)

symmetrical point for the vertex

46.

What are the coordinates of the vertex?

a)

$\left(0,\ -5\right)$

b)

$\left(1,\ 0\right)$

c)

$\left(3,\ 4\right)$

d)

$\left(5,\ 0\right)$

47.

Which best describes the vertex of a parabola?

a)

Any point on the parabola.

b)

A point on the x-axis.

c)

The highest or lowest point of a parabola

d)

A point on the y-axis.

48.

What is the range of the function?

a)

$\left[3,\ \infty\right)$

b)

$\left(-\infty,\ 3\right]$

c)

$\left(-\infty,\ \infty\right)$

d)

$\left[-1,\ 5\right]$

49.

What is the domain of the function?

a)

$\left[3,\ \infty\right)$

b)

$\left(-\infty,\ 3\right]$

c)

$\left(-\infty,\ \infty\right)$

d)

$\left[-1,\ 5\right]$

50.

What is the range?

a)

$\left[-3,\ \infty\right)$

b)

$\left[-1,\ \infty\right)$

c)

$\left(-\infty,\ \infty\right)$

d)

$\left(-\infty,\ -1\right]$

51.

What is another word for x-intercepts?

a)

Zeros

b)

y-intercept

c)

Maximum

d)

Vertex

52.

When a parabola opens downward the vertex is

a)

a minimum

b)

a maximum

c)

a vertex

d)

a parabola

53.

A parabola has a vertex at (-3,2). Where is the axis of symmetry?

a)

y = -2

b)

x = 3

c)

x = -3

d)

y = 2

54.

How many solutions does this graph have?

a)

one

b)

two

c)

no solutions

d)

three

55.

Which of the statements about the graph is FALSE?

a)

The vertex is a maximum

b)

There are two zeros at

(-3, 0) and (3, 0)

c)

The y-intercept is (0, 18)

d)

The range is

$\left[18,\ \infty\right)$

56.

What is the significance of the ordered pair (0, -2) to the graph?

a)

It is the vertex

b)

It is an x-intercept

c)

It is the y-intercept

d)

It is the axis of symmetry

57.

What is the significance of the ordered pair (2, -4) to the graph?

a)

It is the vertex

b)

It is an x-intercept

c)

It is the y-intercept

d)

It is the axis of symmetry

58.

A quadratic function can have how many x-intercepts? Choose all that apply:

a)

None

b)

One

c)

Two

d)

Three

59.

Which is the mirror point of $\left(0,\ -3\right)$ ?

(Hint, where would it be reflected over the axis of symmetry?)

a)

$\left(0,\ -3\right)$

b)

$\left(1,\ -4\right)$

c)

$\left(-1,\ 0\right)$

d)

$\left(3,\ 0\right)$

e)

$\left(2,\ -3\right)$

60.

Which is the mirror point of the y-intercept?

a)

$\left(0,\ -5\right)$

b)

$\left(1,\ 0\right)$

c)

$\left(-5,\ 0\right)$

d)

$\left(5,\ 0\right)$

e)

$\left(6,\ -5\right)$

61.

Which description best fits the transformation of f(x)=x² into f(x) =(x-5)²+3 ?

a)

Opens up, shifts to the right 5, and shifts up 3

b)

Is narrow, shifts left 5 and up 3

c)

Shifts right 5 and down 3

d)

Opens down and shifts up 3

62.

What are the transformations of the function: $f\left(x\right)=\left(x-3\right)^2-5$

a)

Right 3

UP 5

b)

Right 3

Down 5

c)

Left 3

Up 5

d)

Left 3

Down 5

63.

What is the vertex of the function:

$f\left(x\right)=\frac{1}{5}\left(x-9\right)^2+8$

a)

$\left(-9,8\right)$

b)

$\left(9,8\right)$

c)

$\left(\frac{1}{5},9\right)$

d)

$\left(-\frac{1}{5},-9\right)$

64.

What is the vertex of the function:

$f\left(x\right)=-4\left(x-1\right)^2$

a)

$\left(4,-1\right)$

b)

$\left(-4,1\right)$

c)

$\left(-1,0\right)$

d)

$\left(1,0\right)$

65.

What is the axis of symmetry of the function:

$f\left(x\right)=\frac{1}{3}\left(x-4\right)^2-5$

a)

$x=-5$

b)

$x=4$

c)

$x=-4$

d)

$x=5$

66.

Does the parabola
f(x)=4(x-2)² + 3
open up or down?

a)

up

b)

down

67.

What is the axis of symmetry for
f(x)=4(x-2)² + 3

a)

4

b)

2

c)

x = -2

d)

x = 2

68.

What causes the graph of y = x² to open downward?

a)

multiply the x² by a fraction

b)

multiply the x² by a decimal

c)

multiply the x² by a negative number

d)

multiply the x² by a number greater than 1

69.

What is the vertex of the parabola: y=2(x-3)²+4

a)

(3,4)

b)

(-3,4)

c)

(3, -4)

d)

(-3,-4)

70.

Which equation is graphed above?

a)

$y=-\left(x-1\right)^2+4$

b)

$y=\left(x-1\right)^2+4$

c)

$y=-\left(x-4\right)^2+1$

d)

$y=\left(x-4\right)^2+1$

71.

Find the factors of:

$x^2+7x+12$

(a)

72.

What is the first question you ask yourself when factoring a polynomial?

a)

How many terms does it have?

b)

Is there a GCF?

c)

What strategy should I use?

d)

Why do I have to learn this?!?!?!

73.

8r³ - 16r²

a)

4r²(2r - 4)

b)

8r²(r - 2)

c)

8(r³ - r²)

d)

4(r³ - 2r²)

74.

$7r^3-8r^2+42r-48$

a)

$(r^2+6)(7r+8)$

b)

$(r^2+6)(7r-8)$

c)

$(r^2+6)(r^2+8)$

d)

$(r^2+6)(7r+6)$

75.

$x^3-5x^2+5x-25$

a)

$(x^2-5)(x-5)$

b)

$(x^2+5)(x-5)$

c)

$(x^2+5)(x+5)$

d)

$(x^2-1)(x-25)$

76.

Factor by grouping: $x^3+7x^2-2x-14$

a)

$(x^2-2)(x-7)$

b)

$(x^2+2)(x-7)$

c)

$(x^2+2)(x+7)$

d)

$(x^2-2)(x+7)$

77.

What is the greatest common factor of 14 and 35?

a)

2

b)

7

c)

8

d)

5

78.

What does GCF mean?

a)

Great Cookie Fever

b)

Greatest Common Factor

c)

Greatest Common Multiple

d)

Greatest Compared Factor

79.

Which is a NOT a factor of 9?

a)

0

b)

1

c)

3

d)

9

80.

What are the factors of 24?

a)

2, 4, 6, 8, 12

b)

1, 2, 3, 4, 6, 8, 10, 12, 24

c)

1, 2, 3, 4, 5, 6, 7, 12, 24

d)

12, 24, 3, 4, 2, 8, 6, 1

81.

Factor:
x² + 5x - 24

a)

(x - 8)(x + 3)

b)

(x + 8)(x - 3)

c)

(x + 6)(x - 4)

d)

(x + 12)(x - 2)

82.

Factor $k^2-2k-24$

a)

$(k-4)(k+6)$

b)

$(k+4)(k+6)$

c)

$(k+6)(k-1)$

d)

$(k+4)(k-6)$

83.

If a trinomial, ax²+ bx + c, has a negative "c" value, what do you know about the signs in its binomial factors.

a)

The signs are both +.

b)

The signs are one + and one -

c)

The signs are both -

84.

$x^4-81$

a)

$\left(x^2-9\right)\left(x^2+9\right)$

b)

$\left(x^2+9\right)\left(x-3\right)\left(x+3\right)$

c)

$\left(x^4-9\right)\left(x^4+9\right)$

d)

$\left(x^2-9\right)\left(x^2-9\right)$

85.

Factor: x³+ 1

a)

(x + 1)³

b)

(x+1)(x²- x + 1)

c)

(x - 1) (x² + x - 1)

d)

(x + 1)(x² - 2x + 1)

86.

Factor:

64 - 27a³

a)

(4-3a)(9a²+12a+16)

b)

(3a-4)(3a²+12a+16)

c)

(4-3a)(3a²+12a+16)

d)

(4-3a)³

87.

Factor:

x³ - 343

a)

(x + 7) (x² - 7x + 49)

b)

(x² + 1) (x - 343)

c)

(x - 7) (x² + 7x + 49)

d)

(x² - 343) (x + 1)

88.

Factor:

2x³ + 128

a)

2(x³ + 64)

b)

(x + 4)(x² - 4x + 16)

c)

2(x - 4)(x² + 4x + 16)

d)

2(x + 4)(x² - 4x + 16)

89.

Factor:

4x² - 25

a)

(2x + 5) (2x - 5)

b)

(2x - 5)²

c)

(2x + 5)²

d)

2x + 5(2x - 5)

90.

Factor:
x²+ 7x - 30

a)

(x + 10)(x - 7)

b)

(x - 10)(x + 3)

c)

(x + 10)(x + 3)

d)

(x + 10)(x - 3)

91.

Factor completely.
3x²- 9x -120

a)

3(x - 8)(x + 5)

b)

3(x + 8)(x - 5)

c)

(3x + 8)(x - 5)

d)

(3x - 8)(x + 5)

92.

Factor:

25x² - 36y²

a)

5x + 6y(5x - 6y)

b)

(5x + 6y) (5x - 6y)

c)

(5x + 6y)²

d)

(5x - 6y)²

93.

Factor:
$3x^2-75y^2$

a)

$3\left(x-5y\right)\left(x+5y\right)$

b)

$3\left(x^2-25y^2\right)$

c)

$\left(x^2-25y^2\right)$

d)

$3\left(x^2-5y^2\right)\left(x^2-5y^2\right)$

94.

Factor:
x²+ 7x - 30

a)

(x + 10)(x - 7)

b)

(x - 10)(x + 3)

c)

(x + 10)(x + 3)

d)

(x + 10)(x - 3)

95.

Factor
a² - a - 12

a)

(a - 4)(a + 3)

b)

(a + 6)(a - 4)

c)

(a - 6)(a + 4)

d)

(a + 4)(a - 3)

96.

Factor
r² -16r + 60

a)

(r - 15)(r + 4)

b)

(r - 6)(r + 10)

c)

(r - 6)(r - 10)

d)

(r +30)(r - 2)

97.

Factor
x²-16x + 48

a)

(x - 12)(x - 4)

b)

(x + 6)(x - 8)

c)

(x + 12)(x - 4)

d)

(x -16)(x - 3)

98.

Factor
3a² + 4a + 1

a)

(7a-10)(a-8)

b)

Not factorable

c)

(3a+1)(a+1)

d)

(3a-1)(a-1)

99.

Factor completely.
2n² + 13n + 15

a)

(5n - 9)(n - 3)

b)

(3n + 7)(n + 4)

c)

(2n + 3)(n + 5)

d)

Not factorable

100.

Factor
3v² - 4v - 7

a)

(3v-7)(v+1)

b)

3(v-7)(v-1)

c)

(3v+1)(v-9)

d)

(3v+1)(v-10)

101.

Factor completely:
3x² + 18x +15
Hint: Factor GCF first.

a)

3(x² + 6x + 5)

b)

(x + 5)(x + 1)

c)

3(x + 5)(x + 1)

d)

Prime

102.

Factor completely.
5x²-15x+10

a)

(5x - 2)(x - 5)

b)

5(x - 2)(x + 1)

c)

(5x + 2)(x + 5)

d)

5(x - 2)(x - 1)

103.

Factor Completely: 3n² - 15n + 18

a)

(n - 2)(n - 3)

b)

3(n + 2)(n + 3)

c)

(3n - 9)(n - 2)

d)

3(n - 3)(n - 2)

104.

Question 1

a)

A

b)

B

c)

C

d)

D

105.

Question 2

a)

A

b)

B

c)

C

d)

D

106.

Question 3

a)

A

b)

B

c)

C

d)

D

107.

Question 4

a)

A

b)

B

c)

C

d)

D

108.

Question 5

a)

A

b)

B

c)

C

d)

D

109.

Question 6

a)

A

b)

B

c)

C

d)

D

110.

Question 7

a)

A

b)

B

c)

C

d)

D

111.

Question 8

a)

A

b)

B

c)

C

d)

D

112.

Question 9

a)

A

b)

B

c)

C

d)

D

113.

Question 10

a)

A

b)

B

c)

C

d)

D

114.

Question 11

a)

A

b)

B

c)

C

d)

D

115.

Question 12

a)

A

b)

B

c)

C

d)

D

116.

Question 13

a)

A

b)

B

c)

C

d)

D

117.

Question 14

a)

A

b)

B

c)

C

d)

D

118.

Question 15

a)

A

b)

B

c)

C

d)

D

119.

Question 16

a)

A

b)

B

c)

C

d)

D

120.

Question 17

a)

A

b)

B

c)

C

d)

D

121.

Question 18

a)

A

b)

B

c)

C

d)

D

122.

Factor x² – 16.

a)

(x + 2)(x – 8)

b)

(x – 4)(x – 4)

c)

(x + 4)(x + 4)

d)

(x + 4)(x – 4)

123.

x²- 400

a)

( x - 200) ( x + 200)

b)

( x + 20) ( x + 20)

c)

Prime

d)

( x - 20) ( x + 20)

124.

100m²n² - 81p²

a)

Not Factorable

b)

(10mn - 9p)(10mn + 9p)

c)

(10mn² - 9p)(10mn² + 9p)

d)

(25mn - 8p)(25 + 8p)

125.

32n² - 50

a)

(16n - 25)(16n + 25)

b)

2(8n - 25)(8n + 25)

c)

2(4n + 5)(4n - 5)

d)

Not Factorable

126.

The difference of squares says

a)

a² - b² =
(a + b)(a - b)

b)

a² + b² =
(a + b)(a - b)

c)

a² + b² =
(a + b)(a + b)

d)

a² - b² =
(a - b)(a - b)

127.

Which of the following cannot be factored using difference of squares?

a)

4x² - 121

b)

16 - 25x²

c)

m² - n²

d)

36x² - 54

128.

Which of the following cannot be factored using difference of squares?

a)

x²y² - 16

b)

x² - 25y

c)

n⁴ - 36

d)

1 - x²

129.

Factor by rearrangin to use difference of squares
-64 + x²

a)

(x-8)(x+8)

b)

(8-x)(8+x)

c)

(-8+x)(-8-x)

d)

(x-64)(x+64)

130.

Factor by rearranging and using difference of squares
-100 + 49m²

a)

(49m -10)(49m +10)

b)

(-10 + 7m)(-10 - 7m)

c)

(7m - 10)(7m + 10)

d)

(10 - 7m)(10 + 7m)

131.

What is the vertex for the following quadratic?

$f\left(x\right)=-3\left(x+1\right)^2-5$

(a)

132.

What is the vertex for the following quadratic?

$f\left(x\right)=x^2-4$

(a)

133.

What is the vertex for the following quadratic?

$f\left(x\right)=-2\left(x-5\right)^2$

(a)

134.

What is the vertex for the following quadratic?

$f\left(x\right)=\left(x-4\right)^2-4$

(a)

135.

What is the vertex for the following quadratic?

$f\left(x\right)=\left(x-5\right)^2+2$

(a)

136.

What is the vertex for the following quadratic

$f\left(x\right)=-x^2+8x-15$

(a)

137.

What is the vertex for the following quadratic (no spaces in your answer)

$f\left(x\right)=-x^2+7x-12$

(a)

138.

What is the vertex for the following quadratic (no spaces in your answer)

$f\left(x\right)=x^2-3x-4$

(a)

139.

What is the vertex for the following quadratic (no spaces in your answer)

$f\left(x\right)=-\left(x-5\right)\left(x-1\right)$

(a)

140.

What is the vertex for the following quadratic (no spaces in your answer)

$f\left(x\right)=-\left(x+\frac{9}{2}\right)^2+\frac{1}{4}$

(a)

141.

What is the vertex for the following quadratic (no spaces in your answer)

$f\left(x\right)=-\left(x+2\right)\left(x+1\right)$

(a)

142.

What is the vertex for the following quadratic (no spaces in your answer)

$f\left(x\right)=-\frac{1}{3}\left(x+6\right)\left(x+4\right)$

(a)

143.

Which form best describes the quadratics?

$f\left(x\right)=\left(x-2\right)\left(x+1\right)$

a)

Factored Form

b)

Vertex Form

c)

Standard Form

d)

None of the Above

144.

Which form best describes the quadratics?

$f\left(x\right)=-\frac{1}{2}\left(x+2\right)^2-3$

a)

Factored Form

b)

Vertex Form

c)

Standard Form

d)

None of the Above

145.

Which form best describes the quadratics?

$f\left(x\right)=12\left(x-3\right)^2$

a)

Factored Form

b)

Vertex Form

c)

Standard Form

d)

None of the Above

146.

Which form best describes the quadratics?

$f\left(x\right)=-3x^2+2x-12$

a)

Factored Form

b)

Vertex Form

c)

Standard Form

d)

None of the Above

147.

Which form best describes the quadratics?

$f\left(x\right)=\left(x-2\right)\left(x+10\right)$

a)

Factored Form

b)

Vertex Form

c)

Standard Form

d)

None of the Above

148.

If given the equation y = 3(x + 5)² - 4, what is the vertex of the parabola?

a)

(5, -4)

b)

(-5, -4)

c)

(-15, -4)

d)

(15, -4)

149.

Identify the vertex.

a)

(5, 2)

b)

(5, -2)

c)

(-5, 2)

d)

(-5, -2)

150.

The axis of symmetry line passes through which point?

a)

y-intercept

b)

any random point

c)

vertex

d)

symmetrical point for the vertex

151.

What is the equation of this graph?

a)

f(x) = (x -5)² + 1

b)

f(x) = (x - 1)² - 5

c)

f(x) = (x + 1)² - 5

d)

f(x) = (x + 5)² +1

152.

What is the green dashed line called?

a)

roots or x-intercepts

b)

parabola

c)

axis of symmetry

d)

line of dashes

153.

The graph of a quadratic function is called a

a)

Parabola

b)

Vertex

c)

Axis of Symmetry

d)

Vertex Form

154.

What causes the graph of y = x² to open downward?

a)

multiply the x² by a fraction

b)

multiply the x² by a decimal

c)

multiply the x² by a negative number

d)

multiply the x² by a number greater than 1

155.

Which of the following equations matches vertex form of a quadratic?

a)

ax + by = c

b)

y = a(x - h)² + k

c)

y = ax² + bx + c

d)

y = mx + b

156.

Which equation is graphed above?

a)

$y=-\left(x-1\right)^2+4$

b)

$y=\left(x-1\right)^2+4$

c)

$y=-\left(x-4\right)^2+1$

d)

$y=\left(x-4\right)^2+1$

157.

Which of the following equations matches standard form of a quadratic?

a)

ax + by = c

b)

y = a(x - h)² + k

c)

y = ax² + bx + c

d)

y = mx + b

158.

Which of the following shows
f(x) = x² + 12x - 2
written in vertex form?

a)

f(x) = (x + 6)² + 142

b)

f(x) = (x + 6)² - 34

c)

f(x) = (x + 6)² - 38

d)

f(x) = (x + 6)² + 34

159.

Which of the following shows
f(x) = x² - 8x + 1
written in vertex form?

a)

f(x) = (x - 4)² - 15

b)

f(x) = (x - 4)² + 17

c)

f(x) = (x - 4)² - 17

d)

f(x) = (x - 4)² + 65

160.

Convert f(x) = 4x² - 32x + 2 to vertex form.

a)

f(x) = 4(x + 4)² - 62

b)

f(x) = 4(x - 4)² - 62

c)

f(x) = 4(x - 8)² - 62

d)

f(x) = 4(x + 8)² - 62

161.

Identify the vertex and whether the graph opens up or down.

a)

(5, 2); opens up

b)

(5, 2); opens down

c)

(-5, 2); opens up

d)

(-5, 2); opens down

162.

Which equation has a vertex of (-3, 4)?

a)

y = 2(x+3)²+ 4

b)

y = (x+3)² - 4

c)

y = (x-3)² + 4

d)

y = 2(x - 3)² + 4

163.

Does the parabola
f(x)=4(x-2)² + 3
open up or down?

a)

up

b)

down

164.