Free Printable ALG II - Graphs of QUADRATICS (Vertex, Standard &Factored) form

1.

In what form is the quadratic:

$y=\left(x+3\right)\left(x-3\right)$ written?

a)

standard form

b)

vertex form

c)

factored form

2.

Given the quadratic:

y=\left(x+3\right)\left(x-3\right)

Find the x-intercepts.

a)

0 and 3

b)

3 and -3

c)

0 and -9

d)

only 3

3.

Given the quadratic:

y=3\left(x+2\right)\left(x+6\right)

Find the x-intercepts.

a)

2 and 6

b)

-3 and -6

c)

-2 and 6

d)

-6 and -2

4.

Given the quadratic:

y=3\left(x+2\right)\left(x+6\right)

Find the value of

x\ =\ \frac{\left(p+q\right)}{2}

(a)

5.

Find the axis of symmetry of the quadratic below:

y=-2x^2+8x+10

leave no spaces in your answer and include x=

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

(a)

6.

What is the vertex of the quadratic:

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

a)

(3,-3)

b)

(-4,-3)

c)

(3,3)

d)

(-3,-3)

7.

In what form is the quadratic:

$y=-4\left(x+3\right)^2-6$ written ?

a)

standard form

b)

vertex form

c)

factored form

8.

Will the quadratic below have a maximum or minimum?

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

a)

maximum

b)

minimum

9.

Which of the following quadratics are in vertex form?

Check all that apply.

a)

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

b)

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

c)

$y=\left(x+7\right)\left(x-9\right)$

d)

$y=4x^2+2x-9$

e)

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

10.

Which of the following quadratics are in factored form?

Check all that apply.

a)

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

b)

$y=\left(x+6\right)\left(x-9\right)$

c)

$y=4x^2+2x-9$

d)

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

11.

What is the y-intercept of the quadratic below?

y=3x^2-2x+6

a)

6

b)

1/3

c)

-6

d)

-1/3

12.

What is the y-intercept?

f(x) = -2x² + 4x - 6

a)

6

b)

-6

c)

1

d)

-1

13.

Identify the vertex

a)

(-1, -9)

b)

(0, -8)

c)

(-4, 0)

d)

(0, 0)

14.

Does the graph of

y = 2(x + 5)² + 2

have a minimum or a maximum?

a)

Minimum

b)

Maximum

15.

What is the formula to find the axis of symmetry?

a)

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

b)

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

c)

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

d)

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

16.

Given: y = 2(x - 5)² + 6, type the vertex as an ordered pair.

(a)

17.

Which quadratic equation models the parabola shown?

a)

y = (x-2)(x-5)

b)

y = (x+2)(x+5)

c)

y = -(x+2)(x+5)

d)

y = -(x-2)(x-5)

18.

What are the x-intercepts of the quadratic?

a)

2 and 4

b)

-2 and -5

c)

2 and 5

d)

-2 and -4

19.

Which quadratic equation models the parabola shown?

a)

y = (x-2)(x+5)

b)

y = (x+2)(x+5)

c)

y = -(x-2)(x-5)

d)

y = -(x+2)(x+5)

20.

What is the name of this form:

y = a(x - h)² + k

a)

vertex form

b)

standard form

c)

factored form

21.

A parabola has a vertex at (-3, 2).

Where is the axis of symmetry?

a)

y = -3

b)

x = 3

c)

x = -3

d)

y = 2

22.

Maximum or Minimum

a)

Maximum

b)

Minimum

23.

What is the equation of the axis of symmetry?

a)

y = 3

b)

x = 3

c)

x = -3

d)

(3,-1)

24.

Which function has a maximum at (2, 0)?

a)

b)

c)

d)

25.

What is the vertex?

a)

(-3, 0)

b)

(3, 0)

c)

(0, 18)

d)

(18, 0)

26.

Name the x-intercept(s)

a)

0

b)

2 and 4

c)

4 and 0

d)

(2, 4)

27.

What is the y-intercept of the quadratic function?

a)

2

b)

4

c)

-2

d)

0

28.

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

29.

What is the equation for the axis of symmetry for the quadratic function shown?

a)

y = -3

b)

x = -3

c)

x = 5

d)

y = 5

30.

What is the green dashed line called?

a)

x-intercepts

b)

parabola

c)

axis of symmetry

d)

the vertex

31.

The axis of symmetry is a line that goes through the...

a)

y-intercept

b)

any random point

c)

vertex

d)

x-axis or y-axis

32.

Does the parabola open UP or DOWN?

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

a)

UP

b)

DOWN

33.

What are the green dots called?

a)

y-intercepts

b)

maximum

c)

minimum

d)

x-intercepts

34.

Which of the following quadratics are WIDER than the standard quadratic ?

Check all that apply.

a)

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

b)

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

c)

$y=\left(x+6\right)\left(x-9\right)$

d)

$y=4x^2+2x-9$

e)

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

35.

Which of the following quadratics have a REGULAR WIDTH? (look at the 'a' value)

Check all that apply.

a)

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

b)

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

c)

$y=\left(x+6\right)\left(x-9\right)$

d)

$y=4x^2+2x-9$

e)

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

36.

Find the axis of symmetry for

f(x) = x²- 8x + 15. Remember to calculate -b/2a

a)

x = -4

b)

x = 4

c)

y = 4

d)

y = -4

37.

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

a)

4

b)

2

c)

x = -2

d)

x = 2

38.

What is the equation for axis of symmetry?

a)

y=3

b)

x=3

c)

x=5

d)

x=1

39.

What is the y-intercept of this parabola?

a)

(−1, 3)

b)

(5, 0)

c)

(−2, 5)

d)

(0, 5)

40.

What is the range of this quadratic?

a)

[3, inf)

b)

(-inf, 3]

c)

(-inf, inf)

d)

(-inf, 2]

41.

What is the green dot on the parabola called?

a)

vertex

b)

root

c)

dot

42.

The best form of a quadratic to find the Y-intercept.

a)

Factored Form

b)

Vertex Form

c)

Standard Form

43.

The best form of a quadratic to find the vertex.

a)

Factored Form

b)

Vertex Form

c)

Standard Form

44.

The best form of a quadratic to find the X-intercepts.

a)

Factored Form

b)

Vertex Form

c)

Standard Form

45.

What is the y-intercept of this parabola?

a)

(−1, 3)

b)

(5, 0)

c)

There isn't one

d)

(0, 5)

46.

What is the vertex of this parabola?

a)

(−1, 3)

b)

(−3, 11)

c)

(−2, 5)

d)

(0, 5)

47.

What is the axis of symmetry of the quadratic below: Remember -b/2a

$y=3x^2-6x+8$

Leave NO spaces in your answer.

(a)

48.

What is the vertex of the function

y\ =\ -4\left(x\ +7\right)^2\ -\ 8

?

(a)

49.

Given: y = 1/2(x + 4)² - 5,

Find the axis of symmetry.

a)

y = 4

b)

x = -4

c)

x = 4

d)

x = -5

50.

Given: y = 1/2(x + 4)² - 5,

The graphed parabola will be:

a)

Wider

b)

More narrow

c)

Regular width

51.

Find the y intercept: (remember to ignore the x's and multiply)

$y=-2\left(x-1\right)\left(x+3\right)$

What is the value of c?
answer should be ONE number with no spaces

(a)

52.

What is the vertex of the quadratic:

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

a)

(0,-3)

b)

(-4,-3)

c)

(-4,3)

d)

(-3,0)

53.

Match the following.

a)

Standard Form

1.

$f\left(x\right)=ax^2+bx+c$

b)

Vertex Form

2.

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

c)

Intercept Form

3.

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

54.

Match the following

a)

$f(x)=(x-3)(x-1)$

1.

Which form would you use if you want to find the x-intercepts?

b)

$f(x)=x^2-4x+3$

2.

Which form would you use if you want to find the y-intercept?

c)

$f(x)=(x-2)^2-1$

3.

Which form would you use if you want to find the vertex?

55.

Match the following

a)

1.

$y=\left(x-6\right)^2+8$

b)

2.

$y=-\left(x+8\right)\left(x-6\right)$

c)

3.

$y=x^2-6x+8$

d)

4.

$y=\left(x-6\right)\left(x+8\right)$

56.

Which function is in standard form?

a)

g(x) = 4x² + 2x + 4

b)

f(x) = -3x + 4

c)

s(x) = 4(x + 1)² + 4

d)

h(x) = -(x + 2)(x - 3)

57.

Which function is in vertex form?

a)

g(x) = 4x² + 2x + 4

b)

f(x) = -3x + 4

c)

s(x) = 4(x + 1)² + 4

d)

h(x) = -(x + 2)(x - 3)

58.

What is the easiest to identify in standard form?

a)

y-intercept

b)

x-intercept(s)

c)

vertex

59.

What is the easiest to identify in vertex form?

a)

y-intercept

b)

x-intercept(s)

c)

vertex

60.

What is the easiest to identify in factored form?

a)

y-intercept

b)

x-intercept(s)

c)

vertex

61.

What is the vertex of the parabola with the equation
f(x) = -2(x - 4)² - 3

a)

(-4, -3)

b)

(4, 3)

c)

(-4, 3)

d)

(4, -3)

62.

What is the standard form of a quadratic?

a)

y = ax²+ bx + c

b)

y = a(x - h)² + k

c)

y = mx + b

d)

y = (x - h)(x - k)

63.

What is the vertex form a quadratic?

a)

y = ax²+ bx + c

b)

y = a(x - h)² + k

c)

y = mx + b

d)

y = (x - h)(x - k)

64.

Given zeros of x = 3 and x = -1, what would the factored forms be?

a)

y=(x - 3)(x - 1)

b)

y=(x + 3)(x -1)

c)

y=(x - 3)(x + 1)

d)

Not enough information

65.

Which equation matches the x-intercepts x=5,-7 ?

a)

y=(x+5)(x-7)

b)

y=(x-5)(x+7)

c)

y=(x+5)(x+7)

d)

y=(x-5)(x-7)

66.

What is another word for zeros?

a)

y-intercepts

b)

roots

c)

vertex

d)

axis of symmetry

67.

What is the axis of symmetry for this parabola?

a)

x = 2

b)

x = - 8

c)

x = -1

d)

y = -1

68.

Which direction does the following equation open? $y=-3\left(x+3\right)\left(x-2\right)$

a)

Down, because the 'a' value is positive.

b)

Up, because the 'a' value is negative.

c)

Down, because the 'a' value is negative.

d)

Up, because the 'a' value is positive.

ALG II - Graphs of QUADRATICS (Vertex, Standard &Factored) form

Total questions: 68

Worksheet time: 2hrs 37mins

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