AnswersCA-Common Core Math II A-CRModeling with Quadratic Equations

Modeling with Quadratic Equations — Unit test Answers

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Which shows the correct substitution of the values a, b, and c from the equation 0 = 4x2 + 2x – 1 into the quadratic formula below?Quadratic formula: x =

Question illustration
A
x = StartFraction negative 2 plus or minus StartRoot 2 squared minus 4(4)(negative 1) EndRoot Over 2(4) EndFraction
Option A
B
x = StartFraction negative 2 plus or minus StartRoot 2 squared minus 4(4)(1) EndRoot Over 2(4) EndFraction
Option B
C
x = StartFraction negative 2 plus or minus StartRoot 2 squared + 4(4)(negative 1) EndRoot Over 2(4) EndFraction
Option C
D
x = StartFraction negative 2 plus or minus StartRoot negative 2 squared minus 4(4)(negative 1) EndRoot Over 2(4) EndFraction
Option D
2
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What is the vertex of the absolute value function below?

Question illustration
A
(4, –1)
B
(1, –4)
C
(1, 4)
D
(4, 1)
3

The sum of a number and its square is 42. Which equation can be used to find the two numbers for which this is true?

A
x2 + x = 42
B
x2 + 2x = 42
C
x2 + x + 42 = 0
D
x2 + 2x + 42 = 0
4

Which statement is true about ?

Question illustration
A
The graph of f(x) has a vertex of (–4, 6).
B
The graph of f(x) is a horizontal stretch of the graph of the parent function.
C
The graph of f(x) opens upward.
D
The graph of f(x) has a domain of x –6.
Option D
5

Solve x2 = 12x – 15 by completing the square. Which is the solution set of the equation?

A
(negative 6 minus StartRoot 51 EndRoot comma negative 6 + StartRoot 51 EndRoot)
Option A
B
(negative 6 minus StartRoot 21 EndRoot comma negative 6 + StartRoot 21 EndRoot)
Option B
C
(6 minus StartRoot 51 EndRoot comma 6 + StartRoot 51 EndRoot)
Option C
D
(6 minus StartRoot 21 EndRoot comma 6 + StartRoot 21 EndRoot)
Option D
6

Solve x2 – 8x = 3 by completing the square. Which is the solution set of the equation?

A
(4 minus StartRoot 19 EndRoot comma 4 + StartRoot 19 EndRoot)
Option A
B
(4 minus StartRoot 11 EndRoot comma 4 + StartRoot 11 EndRoot)
Option B
C
(4 minus StartRoot 8 EndRoot comma 4 + StartRoot 8 EndRoot)
Option C
D
(4 minus StartRoot 3 EndRoot comma 4 + StartRoot 3 EndRoot)
Option D
7

What are the solutions of the quadratic equation (x + 3)2 = 49?

A
x = –2 and x = –16
B
x = 2 and x =
Option B
C
x = 4 and x = –10
D
x = 40 and x = –58
8

Brianna is graphing the function f(x) = x2 + 6x + 5. What x-intercepts should Brianna use to graph f(x)?

A
–5 and –1
B
–5 and 1
C
–1 and 5
D
1 and 5
9

Zacharias is using the quadratic formula to solve the equation 0 = –2x2 + 5x – 3. He begins by substituting as shown.Quadratic formula: x = Substitution:

Question illustration
A
The –5 should be 5.
B
The 52 should be –52.
C
The 2 in the numerator should be –2.
D
The 2 in the denominator should be –2.
10

What are the solutions to x2 + 8x + 7 = 0?

A
x = –8 and x = –7
B
x = –7 and x = –1
C
x = 1 and x = 7
D
x = 7 and x = 8
12

Which equations can be used to find the lengths of the legs of the triangle? Select three options.

A
0.5(x)(x + 2) = 24
B
x(x + 2) = 24
C
x2 + 2x – 24 = 0
D
x2 + 2x – 48 = 0
E
x2 + (x + 2)2 = 100
13

What are the zeros of the function f(x) = x2 + 5x + 5 written in simplest radical form?Quadratic formula: x =

Question illustration
A
x =
Option A
B
x =
Option B
C
x =
Option C
D
x =
Option D
14

Isoke is solving the quadratic equation by completing the square.10x2+40x-13=010x2+40x=13A(x2+4x)=13

A
-13
B
4
C
10
D
40
15

Alessandro wrote the quadratic equation in standard form. What is the value of c in his new equation?

Question illustration
A
Option
Option A
B
Option
Option B
C
Option
Option C
D
Option
Option D
16

What is the first step in solving the quadratic equation -5x2+8=133?

A
taking the square root of both sides of the equation
B
subtracting 8 from both sides of the equation
C
squaring both sides of the equation
D
adding 8 to both sides of the equation
17

A rectangle’s width is 2 meters shorter than its length, l. Its area is 168 square meters. Which equation can be used to find the length of the rectangle?

A
l(l – 2) = 168
B
l(l + 2) = 168
C
2l 2 = 168
D
l 2 = 168
Option D
18

A group of students is given a 10 by 10 grid to cut into individual unit squares. The challenge is to create two squares using all of the unit squares. Their teacher states that after the two new squares are formed, one should have a side length two units greater than the other.

A
x2 + (x – 2)2 = 10
B
x2 + 2x2 = 10
C
x2 + (x – 2)2 = 100
D
x2 + 2x2 = 100
20

A company manufactures 16-oz boxes of cereal. Boxes are randomly weighted to ensure the correct amount. If the discrepancy in weight is more than 0.15 oz, the production is stopped. What is the range of acceptable values for production to continue?

A
15.15 oz to 16.00 oz
B
15.85 oz to 16.00 oz
C
15.85 oz to 16.15 oz
D
16.15 oz to 16.45 oz
21

Which equation results from taking the square root of both sides of (x – 9)2 = 81?

A
x – 9 = ±9
B
x + 9 = ±9
C
x + 3 = ±9
D
x – 3 = ±9
22

Which equations are true for x = –2 and x = 2? Select two optionsx2 – 4 = 0x2 = –4 3x2 + 12 = 04x2 = 162(x – 2)2 = 0

A
x2 – 4 = 0
B
x2 = –4
C
3x2 + 12 = 0
D
4x2 = 16
E
2(x – 2)2 = 0

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