Free Printable Solving Quadratics

1.

Find the zeros of the equation:
(x+10)(x-2) = 0

a)

10 and 2

b)

-2 and 10

c)

-10 and 2

d)

-2 and -10

2.

What are the solutions/zeros/x-intercepts/roots?

(When does this quadratic =0?)

SELECT ALL THAT APPLY

a)

x = -4

b)

x = -1

c)

x = 0

d)

x = 2

3.

Solve by factoring: x² + 3x - 18 = 0

a)

x = -3 and x = 6

b)

x = 3 and x = -6

c)

x = -9 and x = 2

d)

x = 9 and x = -2

4.

Solve by factoring: x² - 9x + 20 = 0

a)

x = -4 and x = -5

b)

x = 20 and x = -9

c)

x = 4 and x = 5

d)

x = -4 and x = 5

5.

What should you do first in solving this equation?

x² + 6x - 13 = 3

a)

Get factored form

b)

Write down: a=1, b=6, c=-13

c)

Make it equal 0 by subtracting 3 on each side

d)

Type it all in a calculator.

6.

$x^2\ +\ 5x\ =\ -6$

Set the equation equal to zero.

a)

$x^2+5x-6=0$

b)

$x^2+5x+6=0$

c)

$x^2=-5x\ -6$

7.

Find the zeros of this quadratic.

a)

b=4/5, b=3

b)

b=4, b=-3

c)

b=1/5, b=3

d)

b=4/5, b=-3

8.

What is another word for zeros?

a)

y-intercepts

b)

roots

c)

vertex

d)

axis of symmetry

9.

How many zeros does this parabola have?

a)

3

b)

2

c)

0

d)

1

10.

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

a)

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

b)

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

c)

a = 4, b = 8, c = 3

d)

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

11.

What is the first step in solving
(x + 2)(x - 3) = 0 ?

a)

Plug in zero for x

b)

Solve for x

c)

FOIL

d)

Set each binomial factor equal to zero

12.

What are the values of x when y = 0? (a)

Choose from the below words

{ -3, 1 }

{ -2 }

{ -3, -1 }

{ 1, 3 }

13.

You are given the factored equation $\left(x+8\right)\left(x-2\right)=0$ . What is the next step to solve for x.

a)

Set $x+8=0$ and $x-2=0$

b)

Nothing the solution is $x=8$ and $x=-2$

c)

Multiply $\left(x+8\right)\left(x-2\right)$

d)

Choose $x+8$ or $x-2$ and write a musical about them

14.

Solve $\left(x+2\right)\left(x-11\right)=0$ for x.

a)

$x=-2$ or $x=-11$

b)

$x=2$ or $x=-11$

c)

$x=2$ or $x=11$

d)

$x=-2$ or $x=11$

15.

Find the product:
(3x + 2)(2x + 4)

a)

6x² + 16x + 8

b)

5x² +11x + 6

c)

5x² + 16x + 6

d)

6x² + 11x + 8

16.

WRITING How can you use a graph to find the number of solutions of a quadratic equation?

The number of solutions is the number of (a) of the graph of the related equation.

Choose from the below words

x-intercepts

y-intercepts

maximums

minimums

17.

Describe the number of solutions a quadratic equation has.

Match the following.

a)

Two x-intercepts

1.

2 solutions (roots, zeroes)

b)

One x-intercept

2.

1 solution (root, zero)

c)

0 x-intercepts

3.

No real solutions

(root, zero)

18.

How are solutions, roots, x -intercepts, and zeros related?

a)

The solutions are the y -values that correspond to the roots, x -intercepts, and zeros of an equation.

b)

The solutions are the roots, and are the y -values that correspond to the x -intercepts and the zeros of an equation.

c)

There are two roots or zeros for every x -intercept or solution of an equation.

d)

The solutions are the same as the roots of the equation and are the same as the x -intercepts or zeros of the related equation.

19.

Write $4x^2=12$ in standard form.

20.

THOUGHT PROVOKING

How many different parabolas have −2 and 2 as x-intercepts?

a)

Infinitely Many

b)

1

c)

2

d)

None

e)

Cannot Be Determined Given This Information

21.

Select the answer that has a, b, and c correctly labeled:

y=-x^2+2x-9

a)

a= 1, b= 2, c= -9

b)

a= 2, b= -1, c= 9

c)

a= -9, b= 2, c= -1

d)

a= -1, b= 2, c= -9

22.

Factor completely
n² + 16n + 63

a)

(n-7)(n+4)

b)

(n+7)(n-9)

c)

(n-3)(n-10)

d)

(n+7)(n+9)

23.

What are the green dots called?

a)

axis of symmetry

b)

vertex

c)

parabola

d)

roots or x-intercepts

24.

What shape is the graph of a quadratic?

a)

Hyperbola

b)

Parabola

c)

Straight Line

d)

Circle

25.

An x-intercept is also called...

a)

a root

b)

a solution

26.

1) What type of equation is graphed ?

a)

linear

b)

quadratic

c)

exponential

d)

constant

27.

Given a graph, how can you find the "solutions" to a quadratic?

a)

Call a friend

b)

Plug into a calculator

c)

Solutions are where the quadratic crosses the x-axis

d)

Magic 8 Ball -_-

28.

Choose the correct values for a, b, and c.

$4x^2-5x\ =\ 9$

a)

a = 4

b)

b = 5

c)

c = 9

d)

b = -5

e)

c = -9

29.

Match the following. (20 Points)

a)

(x + 1)(x + 5)

1.

$x^2+6x+5$

b)

(x - 4)(x + 6)

2.

$x^2+2x-24$

c)

(x - 7)(x - 3)

3.

$x^2-10x+21$

30.

Focus Question: How can we use b and c to find the binomial factors of a polynomial $x^2+bx+c$ ? (10 points)

4 lines

31.

Mini Lesson: To factor a trinomial of the form x²+bx+c, you must find two integers that (a) and (b) . (10 points)

Choose from the below words

add to "b"

multiply to "c"

subtract to "b"

add to "c"

multiply to "b"

divide to "b"

divide to "c"

subtract to "a"

32.

Mini Lesson:

x²+ 7x + 12

What two integers have a product of 12 and a sum of 7? (10 points).

a)

2

b)

3

c)

4

d)

5

e)

6

33.

Independent Practice: (15 points)

Factor k²+7x+10

a)

(k+2)(k+5)

b)

(k-2)(k-5)

c)

(k+10)(k+4)

d)

(k+2)(k-5)

34.

Error Analysis

Describe and correct the error in factoring the polynomial. (See photo)

4 lines

35.

Summarize: (10 points)

See Photo

4 lines

36.

a)

(x - 12)(x - 3)

b)

(x + 3)(x + 12)

c)

(x + 12)(x - 3)

d)

(x + 3)(x - 12)

37.

a)

(x + 5)(x + 5)

b)

(x + 25)(x + 1)

c)

(x - 5)(x - 5)

d)

(x + 5)(x - 5)

38.

Factor
x²-16x + 48

a)

(x - 12)(x - 4)

b)

(x + 6)(x - 8)

c)

(x + 12)(x - 4)

d)

(x -16)(x - 3)

39.

Match the following. (20 points)

a)

i.

1.

3

b)

ii.

2.

-4

c)

iii.

3.

-2/3

d)

iv.

4.

2

e)

v.

5.

0

40.

Key Idea

(a) - Product Property

Algebra: If a and b are (b) and (c) , then (d) or (e) .

Choose from the below words

Zero

real numbers

ab = 0

a = 0

b=0

41.

In the equation (x + 2)(x - 3) = 0, the binomials are called...? (3 points)

a)

Factors

b)

Products

c)

Multiples

d)

Zeros

42.

Error Analysis - Describe and Correct The Error In Solving The Equation (20 points).

4 lines

43.

When factoring a polynomial...

(3 points)

a)

we first look for a GCF,

b)

which is the

c)

largest monomial term

d)

that can be divided

e)

into every term.

1)

2)

3)

4)

5)

44.

Factoring Polynomials Using the GCF reverses what property? (3 points)

a)

The Distributive Property

b)

The Zero - Property

c)

The Additive Property

d)

The Commutative Property

e)

The Associative Property

45.

What is the GCF of 18 and 24? (5 points)

a)

3

b)

6

c)

8

d)

9

46.

What is the GCF of 18k and 15k^{3 ?}

(5 points)

a)

3k²

b)

3k³

c)

3k

d)

5k

47.

Factor: (5 points)

10x + 15

a)

100x + 150

b)

10(x + 5)

c)

1(10x + 15)

d)

5(2x + 3)

48.

Factor by using GCF: (5 points)

8n³ + 2n²

a)

2n²(4n-1)

b)

2n²(4n + 1)

c)

n²(8n+2)

d)

3n(4n+1)

Solving Quadratics

Total questions: 48

Worksheet time: 12hrs 0mins

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