Free Printable Chapter 3 Review A2

Worksheets

Chapter 3 Review A2

Total questions: 50

Worksheet time: 4hrs 10mins

Name

Class

Date

ax²+bx+c=0 is the standard form of a quadratic equation.

True

False

What should you do first in solving this equation?
x² + 6x - 13 = 3

Get factored form

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

Make it equal 0 by subtracting 3 on each side

Type it all in a calculator.

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

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

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

a = 4, b = 8, c = 3

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

Solve using the Quadratic Formula:

2x² + 2x − 12 = 0

x = −2, 3

x = 2, 3

x = 2, −3

x = −2, −3

What number added would make a perfect square trinomial?

x² - 8x + ______

-4

-64

Factor Completely:
3x² + 18x +15

3(x² + 6x + 5)

(x + 5)(x + 1)

3(x + 5)(x + 1)

Prime

-10

10i

-10i

What is the complex conjugate of 4-3i?

A. 1/(4-3i)

B. 1/(4+3i)

C. -4 + 3i

D. 4 + 3i

Simplify:
i⁷

-i

-1

10.

Solve
3x² - 5 = -446

±√-147

7i√3

±7i√3

-7√3

11.

(5-2i) + (-7+8i)

-2+6i

12+6i

-35-16i²

-35 -16i

12.

Multiply:
(4 – 3i)(-7 – 2i)

A. -23 + 13i

B. -23 - 29i

C. -34 + 13i

D. -34 - 29i

13.

Complete the Square and write in Vertex Form:
f(x) = x² + 6x + 5

(x + 3)² - 4

(x + 6)² - 4

(x + 3x)² - 4

(x + 3)² + 9

14.

Complete the square and write in Vertex Form
f(x) = x² + 4x + 9

f(x) = (x+2)² + 5

f(x) = (x - 2)² + 5

f(x) = (x+4)² + 5

f(x) = (x+2)² - 5

15.

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

(5, -4)

(-5, -4)

(-15, -4)

(15, -4)

16.

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

(3,4)

(-3,4)

(3, -4)

(-3,-4)

17.

Simplify:

(10+ 15i) - (48 - 30i)

58 - 45i

58 - 15i

-38 - 15i

-38 + 45i

18.

Simplify:

8i(2 + 3i) + 6i(2 + i)

-30 - 4i

30 - 28i

-30 + 28i

16 + 48i

19.

What do you do to the b value to correctly complete the square?

square it

divide it by 2 and square the result

divide it by 2 and take the square root of the result

divide it by 2 only

20.

To solve by completing the square, what needs to be moved in this equation?
x² = 9 - 4x

the -4x

the 9

the x²

21.

When factoring
x² - 4x + 4 = 20,
what goes in the blank?
(x - __ )² = 20

22.

When do you use the plus or minus symbol?
±

After taking the square root of both sides

After adding the square to both sides

After taking half of b

After setting the equation equal to zero

23.

Complete the square for
x² + 12x + ____

x² + 12x + 144

x² + 12x + 36

x² + 12x - 36

x² + +12x - 144

24.

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

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

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

a = 4, b = 8, c = 3

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

25.

Use the quadratic formula to find the solutions for

y = -x² - 5x + 12

-4.9 and -0.1

-8.54 and 8.54

-0.45 and 3.55

-6.77 and 1.77

26.

Solve using the quadratic formula.
2x² - 9x - 35 = 0

x = 7/2, x = -6

x = -5/2, x =5

x = -3/7, x =6

x = -5/2, x = 7

27.

What is this formula?

This is the speed of light formula.

This is the quadratic formula.

This is the zero product property.

This is scary.

28.

Factor: x² – 5x – 24

(x - 5)(x + 19)

(x - 8)(x + 3)

(x - 3)(x + 8)

(x - 19)(x + 5)

29.

The quadratic equation can be used to solve quadratic equations that cannot be factored.

True

False

30.

The discriminant is

ax² + bx + c

b - 4ac

b² - 4ac

b² + 4ac

31.

-5i

-5

32.

If the discriminant equals 0, then the quadratic has:

1 Rational Solution

2 Rational Solutions

No solutions

2 Complex Solutions

33.

If the discriminant is positive but NOT a perfect square, then the quadratic has:

1 Rational Solution

2 Irrational Solutions

2 Rational Solutions

2 Complex Solutions

34.

If the discriminant is negative, then the quadratic has:

1 Rational Solution

2 Rational Solutions

2 Irrational Solutions

2 Complex Solutions

35.

36.

Identify the solution to the system graphed here.

(0, 4) and (0, -2)

(2, -2)

(0 4)

No solution

37.

Find the solution.

(2,3) and (3,4)

(-3,-15) and (4,-8)

(-3,10) and (8,4)

(-8,3) and (-4,10)

38.

Find the solution(s) to the system.

(0,-3)(1,-2)

(0,-3)

(-2,0)(2,0)

No solution

39.

Solve the System using ANY method:

y\ =\ x^2-6x+9

y\ =\ -2x+5

(1, 2)

(2, 1)

(1, 2) and (2, 1)

No solution! It is an Inconsistent System.

40.

Is the point (5, 3) a solution to this nonlinear system?

Yes a solution

No Not a solution

41.

Is the point (2, 7) a solution to this nonlinear system?

Yes a solution

No Not a solution

42.

Which inequality is shown?

y< -x²

y≤ -x²

y> -x²

y≥ -x²

43.

Which inequality is represented by the graph?

y > (x - 3)² - 3

y ≥ (x + 3)² - 3

y > (x + 3)² - 3

y ≥ (x - 3)² - 3

44.

y ≤ (x - 3)² + 3

y < (x + 3)² - 3

y < (x - 3)² - 3

y ≤ (x + 3)² - 3

45.

Find the solution:

y = x² - 4x + 6

y = x + 2

{(3, 1), (6, 4)}

{(-1, 1), (4, 2)}

{(1, 3), (4, 6)}

{(1, 4), (3, 6)}

46.

How many solutions does this system of equations have?

one real solution

two real solutions

no real solutions

infinitely many solutions

47.

Solve the system of Equations:

y= 3

y= x² - 4x + 7

{(2,3), (4,3)}

{(3,2), (3,4)}

{(-2,3)}

{(2,3)}

48.

Which correctly shows the inequality $y\ge-\left(x+2\right)^2-4$ ?

49.

Which correctly shows the inequality $y<x^2-6x+13$ ?

50.

What are the solutions to the graphed system?

{(-6, 0), (-2, 0)}

{(-2,0), (2,0)}

{(0, 2), (2, 0)}

no real solution

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Chapter 3 Review A2

Total questions: 50

Worksheet time: 4hrs 10mins

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