AnswersFL-1200330-Algebra 2 CRModeling with Quadratic Equations

Modeling with Quadratic Equations — Test Answers

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1
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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
2
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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
3

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
4

Which represents the solution(s) of the system of equations, y = x2 – x + 1 and y = x? Determine the solution set by graphing.

A
(1, 1)
B
(0, 1) and (1, 1)
C
(0, 0) and (1, 1)
D
no solutions
5

A function g(x) has x-intercepts at (, 0) and (6, 0). Which could be g(x)?

Question illustration
A
g(x) = 2(x + 1)(x + 6)
B
g(x) = (x – 6)(2x – 1)
C
g(x) = 2(x – 2)(x – 6)
D
g(x) = (x + 6)(x + 2)
6

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
7

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
8

Ramiya is using the quadratic formula to solve a quadratic equation. Her equation is x = after substituting the values of a, b, and c into the formula. Which is Ramiya’s quadratic equation?Quadratic formula: x =

Question illustration
A
0 = x2 + 3x + 2
B
0 = x2 – 3x + 2
C
0 = 2x2 + 3x + 1
D
0 = 2x2 – 3x + 1
9

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
10

A box is to be constructed with a rectangular base and a height of 5 cm. If the rectangular base must have a perimeter of 28 cm, which quadratic equation best models the volume of the box? V = lwhP = 2(l + w)

A
y = 5(28 – x)(x)
B
y = 5(28 – 2x)(x)
C
y = 5(14 – x)(x)
D
y = 5(14 – 2x)(x)
11

Which represents the solution(s) of the graphed system of equations, y = x2 – 2x and y = –2x – 1?

Question illustration
A
(1, –1)
B
(0, 0) and (0, –1)
C
(0, 0) and (2, 0)
D
no solutions
12

What number should be added to both sides of the equation to complete the square? x2 + 12x = 11

Answer not available
13

Which are the roots of the quadratic function f(q) = q2 – 125? Select two options.q = 5q = -5q = 3q = -3q = 25

Question illustration
A
q = 5
Option A
B
q = -5
Option B
C
q = 3
Option C
D
q = -3
Option D
E
q = 25
Option E
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

The first three steps for solving the quadratic equation by completing the square are shown. Fill in the missing number in the last step. 9x2 +54x = 7 9(x2 + 6x) = 7 9(x2 + 6x + 9) = 7 +

Answer not available
16

The graph below shows the height of a projectile t seconds after it is launched. If acceleration due to gravity is –16 ft/s2, which equation models the height of the projectile correctly?h(t) = at2 + vt + h0

Question illustration
A
h(t) = –16t2 + 42t + 5
B
h(t) = –16t2 + 5
C
h(t) = –16t2 + 32
D
h(t) = –16t2 + 32t + 5 ✓ Correct
17

What are the values of a, b, and c in the quadratic equation 0 = 5x – 4x2 – 2?

A
a = 5, b = 4, c = 2
B
a = 5, b = –4, c = –2
C
a = –4, b = 5, c = –2
D
a = 4, b = –5, c = –2
18

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
19

A rectangle has an area of 40 square units. The length is 6 units greater than the width.

A
8 by 5
B
10 by 4
C
11 by 9
D
13 by 7
20

What are the zeros of the quadratic function f(x) = 2x2 – 10x – 3?

A
x = – and x = +
Option A
B
x = – and x = +
Option B
C
x = – and x = +
Option C
D
x = – and x = +
Option D

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