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Math 2 Unit 3 Test - Solving Quadratics

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SRMHS Math 2 Unit 3 Test - Solving Quadratics (Fall 2021)

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A.REI.4.b

NC.M2.A-REI.1

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NC.M1.A-REI.10

NC.M2.A-REI.4.b

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A.REI.4.b

NC.M2.F-IF.8

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A.REI.4.b

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Showing your work!

For any problems that say "show your work," you may choose to do one of the following:

1) Use the "show your work" area to write, draw, or type the math. (There is a math keyboard there.)

2) Do your work on notebook paper (labeled neatly) and give it to me at the end of the test.

Pitanje 1

1.

Solve the quadratic using any method.
x^{2}+15x+56=0
Show your work.

x=8, 7

x=-8, 7

x=8, -7

x=-8, -7

Pitanje 2

2.

How many real solutions does this quadratic equation have? (You do NOT need to find the solutions.)
x^{2}+9x-8=0

2 real solutions

1 real solution

no real solutions

Pitanje 3

3.

All quadratic equations will have at least one imaginary solution.

Tačno

Netačno

Pitanje 4

4.

Solve the following quadratic equation by factoring:
6x^{2}-42x+72=0
Type your two answers in the format: _,_
(Separate your answers with a comma. Do not put any spaces. Do not type x=.)

Pitanje 5

5.

What would be the first step to solving the following quadratic by the Quadratic Formula?
b^{2}-16b+64=19

Add 19 to both sides of the equation.

Divide both sides of the equation by 19.

Enter the equation (as-is) into the y= on the calculator.

Subtract 19 from both sides of the equation.

Pitanje 6

6.

What is the solution of the quadratic equation 2x^{2} - x = 14?
Show your work in the space provided.

\frac{-1\pm\sqrt{111}}{2}

\frac{-1\pm\sqrt{113}}{4}

\frac{1\pm\sqrt{113}}{4}

\frac{1\pm\sqrt{111}}{4}

Pitanje 7

7.

Solve for c by factoring.
Type your two answers in the format: _,_
(Separate your answers with a comma. Do not put any spaces. Do not type x=.)

Pitanje 8

8.

Given the standard form, find the factored form.

(x+6)(x-7)

(x+6)(x+7)

(x-6)(x-7)

(x-6)(x+7)

Pitanje 9

9.

Factor the polynomial:

(x + 5) (x + 2)

(3x + 1) (x + 2)

(x + 3) (x + 2)

(3x + 2) (x + 1)

Pitanje 10

10.

Solve by completing the square. Show your work. Hint: Take out a GCF first.

{ -2 , 6 }

{ -6 , -2 }

{ -6 , 2 }

{ 2 , 6 }

Pitanje 11

11.

Solve the equation by completing the square. Simplify your answer. Use the keypad to the right of the answer blank to type the plus/minus and the square root symbols. Make sure your correct answer is on your work as well.

Pitanje 12

12.

Write the expression below in simplest radical form:

Pitanje 13

13.

Simplify the radical.
\sqrt{-27}

-3i\sqrt{3}

9i\sqrt{3}

3i\sqrt{3}

-3\sqrt{3}

Pitanje 14

14.

Factor the expression (x^{2}-81)

x(x-9)

9x(x-9)

(x-9)^2

(x+9)(x-9)

Pitanje 15

15.

Solve the equation by using square roots. 3x^{2}=21

x=7,-7

x=\pm \sqrt{7}

x=\pm \frac{\sqrt{21}}{3}

x=-\sqrt{7},\sqrt{21}

Pitanje 16

16.

Factor out the GCF. 6x^{5}+8x^{3}

2(3x^{5}+4x^{3})

2x(3x^{4}+4x^{2})

2x^{3}(3x^{2}+4)

6x^{3}(x^{2}+2)

Pitanje 17

17.

Factor completely. Write your final answer without spaces! Show your work!

Pitanje 18

18.

Solve the equation by graphing on this graphing calculator. Type your solutions in the "show your work" area for full credit. (Just having the correct graph WITHOUT identifying the solutions will NOT be full credit.)
y=4x^{2}+3x-1

Objavili smo novi i poboljšani tip pitanja za grafički prikaz! Studenti više neće moći odgovoriti na ovo pitanje.

Pitanje 19

19.

Choose the number that fills in the blank to complete the square.
x^{2}+12x+____

144

36

12

6

Pitanje 20

20.

Identify the factors, and solution(s) of the quadratic equation.
Hint: You should only use four things (two for factors and two for solutions

x = -3
(2x - 1)
no solution
(x - 1)
x = ½
(x + 3)
x = 1

Factors
Solution(s)