Free Printable Algebra 1: Chapter 9: L1-L3: Solving Quadratic Equations

1.

Solve the following quadratic equation...

x² + 3x + 2 = 0

a)

x = -1

x = -2

b)

x = 1

x = 2

c)

x = -1

x = 2

d)

x = 1

x = -2

2.

Solve the following quadratic equation...

x² + 7x + 12 = 0

a)

x = -2

x = -6

b)

x = -3

x = -4

c)

x = -1

x = -12

d)

x = 2

x = 6

3.

Solve the following quadratic equation...

x² + 9x + 20 = 0

a)

x = -2

x = -10

b)

x = -5

x = -4

c)

x = -1

x = -20

d)

x = 4

x = 5

4.

Solve the following quadratic equation...

x² + 4x - 32 = 0

a)

x = 8

x = -4

b)

x = -8

x = 4

c)

x = -2

x = 16

d)

x = 2

x = -16

5.

Solve by taking the square root: -5x² = -50

a)

± 5

b)

± 10

c)

± √10

d)

-10

6.

Solve by taking the square root: x² = 16

a)

± 4

b)

± 8

c)

4

d)

8

7.

What is the equation for axis of symmetry?

a)

y=3

b)

x=3

c)

x=5

d)

x=1

8.

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

9.

Solve by factoring: x² = 7x + 18

a)

-7 and -18

b)

9 and 2

c)

9 and -2

d)

2 and 7

10.

Solve by factoring: 2x²+ 7x + 6 = 0

a)

x= 3/2 and x = 2

b)

x = -3/2 and x = -2

c)

x = 6 and x = 7

d)

x = -6 and x = -7

11.

Solve for x:

(x-5)(x+6)=0

a)

{5,5 }

b)

{ -5,-5 }

c)

{ -5,-6 }

d)

{5,-6 }

12.

Solve by factoring:
x² - 9x = 0

a)

9

b)

0, 9

c)

-9, 0

d)

-9

13.

What property would you use to solve the following?
(x-3)(x+2)=0

a)

Commutative Property

b)

Associative Property

c)

Zero Product Property

d)

Inverse Property

14.

Solve using Zero-Product Property.

(2x - 2)(5x + 5) = 0

a)

x = -1

b)

x = -1 or x = 1

c)

x = 1

d)

x = -2 or x = 5

15.

Solve by factoring.

n² - 2n = 0

a)

n = 2 and 0

b)

n = -2 and 0

c)

n = 2

d)

n = 0

16.

Solve: $20x=5x^2+20$ by factoring

a)

$x=0$ and $x=2$

b)

$x=-2$

c)

$x=2$

d)

$x=2$ and $x=-2$

17.

Find the zeros.

a)

0 and 4

b)

0 and -4

c)

0

d)

-4

18.

x²- 25

a)

( x + 5 ) ( x - 5 )

b)

( x - 5 ) ( x - 5 )

c)

( x + 5 ) ( x + 5 )

d)

Prime

19.

Solve by finding square roots and simplify completely:
$2x^2=20$

a)

$x=\pm10$

b)

$x=\sqrt{10}$

c)

$x=\pm\sqrt{10}$

d)

No real solutions

20.

Solve by finding square roots and simplify completely:
$x^2-16=0$

a)

$x=\pm16$

b)

$x=4$

c)

$x=\pm4$

d)

No real solutions

21.

Determine the values of
a, b, and c for
the quadratic equation:
4x² – 8x = 3

a)

A.

a = 4, b = -8, c = 3

b)

B.

a = 4, b =-8, c =-3

c)

C.

a = 4, b = 8, c = 3

d)

D.

a = 4, b = 8, c = -3

22.

How many zeros does this parabola have?

a)

3

b)

2

c)

0

d)

1

23.

What are the solutions of this graph?

a)

x=-2 and x=3

b)

x=-1/2 and x=-6

c)

x=-2 and x=-6

d)

x=3 and x=-6

24.

How many solutions (x-intercepts) does the quadratic have?

a)

Two Solutions

b)

One Solution

c)

0 Solutions

d)

I don't know

25.

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)

26.

Find the zeros of the quadratic equation y=4(x+9)²-36

a)

x=-9+√6 & x=-9-√6

b)

x=3 & x=-3

c)

x=-6 & x=-12

d)

so solution

27.

What is the vertex of the graph?

a)

(2, 4)

b)

(3, -1)

c)

(0, 8)

d)

(4, 2)

28.

$2x\left(x-\ 9\right)=\ 0$
What are the two equations you will create to solve using the zero product property?

a)

2x = 0

b)

x - 9 = 0

c)

2x = 0 OR x - 9 = 0

29.

Which of the following equations represents the vertex form of a quadratic function?

a)

$y=ax^2+bx+c$

b)

$y=a\left(x-b\right)\left(x-c\right)$

c)

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

30.

Find ALL of the X-Intercepts of the following Quadratic Function:

$y=-2\left(x-9\right)\left(x-1\right)$

(Only 1 of them are below)

a)

$\left(0,18\right)$

b)

$\left(1,0\right)$

c)

$\left(-9,0\right)$

d)

$\left(9,0\right)$

e)

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

31.

Find the Axis of Symmetry of the following Quadratic Function:

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

a)

$x=1$

b)

$x=-4$

c)

$x=-2$

d)

$x=-1$

e)

$x=-3$

32.

Find the Vertex of the following Quadratic Function:

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

a)

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

b)

$\left(4,5\right)$

c)

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

d)

$\left(4,3\right)$

e)

$\left(-3,12\right)$

33.

Which quadratic function is represented by the graph?

a)

y = -(x + 1)² - 4

b)

y = -(x + 1)² + 4

c)

y = -(x - 1)² - 4

d)

y = (x + 1)² + 4

34.

Determine the vertex of h(x) = (x - 8)(x + 2)

a)

(-8, 2)

b)

(8, -2)

c)

(3, -25)

d)

(3, 25)

35.

Write the equation of the quadratic function in Intercept Form using the x-intercepts and ANY point on the graph.. Remember: Intercept form is written as y = a(x-p)(x-q)

a)

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

b)

y = -1/2(x - 1)(x + 3)

c)

y = 2(x + 1)(x - 3)

d)

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

36.

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

37.

Which of the following is the correct equation for the given graph?

a)

f(x) = -(x + 2)² - 4

b)

f(x) = -(x - 2)² - 4

c)

f(x) = -3(x - 2)² - 4

d)

f(x) = -3(x + 2)² - 4

38.

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)

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

39.

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

Choose the correct graph of the equation.

a)

b)

c)

d)

40.

If a parabola opens upward and has x-intercepts at (0, 3) and (0, -9), what is the equation?

a)

y = a(x - 3)(x - 9), a > 0

b)

y = a(x - 3)(x + 9), a < 0

c)

y = a(x - 3)(x - 9), a < 0

d)

y = a(x - 3)(x + 9), a > 0

41.

Write an equation of this graph in intercept (factored) form.

a)

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

b)

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

42.

What are the green dots called?

a)

axis of symmetry

b)

vertex

c)

parabola

d)

roots or x-intercepts

43.

Graph the quadratic function

a)

A

b)

B

c)

C

d)

D

44.

Graph the quadratic function

a)

A

b)

B

c)

C

d)

D

45.

Simplify

a)

9

b)

√9

c)

3√9

d)

can't simplify

46.

According to exponent rules, when we multiply the expressions we _______ the exponents.

a)

add

b)

subtract

c)

multiply

d)

divide

47.

Simplify:
√48m⁸n³

a)

2m⁴n²√3

b)

16m⁴n√3n

c)

4m⁴n√3n

d)

4m²n√3m²

48.

Simplify:
-3√375

a)

-15√15

b)

-15√5

c)

-5√75

d)

-5√15

49.

Simplify:
2√80x⁵y⁷

a)

8x²y²√xy

b)

4x²y³√xy

c)

16x⁴y⁶√5xy

d)

8x²y³√5xy

50.

a)

y²z¹⁰√xy

b)

20yz√xy

c)

xy²z¹⁰√y

d)

yz⁶√xy²z²

51.

Simplify:

a)

2√12

b)

4√12

c)

4√3

d)

16√3

52.

Simplify:

a)

2√3√14

b)

4√42

c)

2√42

d)

4√3√14

53.

Simplify:

a)

240

b)

300

c)

340

d)

360

54.

Read the question carefully and choose the correct answer.

a)

A

b)

B

c)

C

d)

D

55.

Simplify.

a)

5x⁸y¹⁰√10x

b)

5x⁴y⁵√10x

c)

5x⁴y⁵√2x

d)

5√2x⁹y¹⁰

56.

Simplify the radical expression

a)

b)

c)

d)

57.

a)

A

b)

B

c)

C

d)

D

58.

Simplify:
(4√5)(7√7)

a)

28√35

b)

4√35

c)

140√7

d)

Cannot be multiplied.

59.

Multiply and simplify. Assume that all variables are positive. $\sqrt{8y^5}\cdot\sqrt{40y^2}$

a)

$8y^3\sqrt{5}$

b)

$8y^3\sqrt{5y}$

c)

$8y\sqrt{5y}$

d)

$8y^3\sqrt{5}$

60.

Multiply and simplify. Assume that all variables are positive. $\sqrt{8y^5}\cdot\sqrt{40y^2}$

a)

$8y^3\sqrt{5}$

b)

$8y^3\sqrt{5y}$

c)

$8y\sqrt{5y}$

d)

$8y^3\sqrt{5}$

61.

Multiply and simplify. Assume that all variables are positive. $\sqrt{7x^5}\cdot\sqrt{42xy^9}$

a)

$7xy\sqrt{6y}$

b)

$7x^2y^2\sqrt{6y}$

c)

$7x^3y^4\sqrt{6y}$

d)

$7xy^3\sqrt{6y}$

62.

$\sqrt{8xy^4}\cdot\sqrt{2x^2y^4}$

a)

$4y^4\sqrt{x}$

b)

$4xy^4\sqrt{x}$

c)

$4xy^8\sqrt{x}$

d)

$2xy^4\sqrt{2x}$

Algebra 1: Chapter 9: L1-L3: Solving Quadratic Equations

Total questions: 62

Worksheet time: 3hrs 13mins

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