Answers CMS 2026-2027 NC Math 1 CREDIT RECOVERYQuadratic Functions and Equations

Quadratic Functions and Equations — Test Answers

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Which function does the graph represent?

f of x is equal to open paren x plus 3 close paren times open paren x plus 7 close paren

f of x is equal to 3 open paren x minus 3 close paren open paren x minus 7 close paren

f of x is equal to open paren x minus 3 close paren times open paren x minus 7 close paren

f of x is equal to 11 open paren x plus 3 close paren open paren x plus 7 close paren

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What is true about the domain and range of the function?

The domain is all real numbers less than or equal to 4, and the range is all real numbers such that negative 3 is less than or equal to x comma x is less than or equal to 1 .

The domain is all real numbers such that negative 3 is less than or equal to x comma x is less than or equal to 1 , and the range is all real numbers less than or equal to 4 .

The domain is all real numbers, and the range is all real numbers less than or equal to 4 .

The domain is all real numbers less than or equal to 4 , and the range is all real numbers.

Which equations can be used to find the lengths of the legs of the triangle? Choose three correct answers.

x squared plus 2 x minus 24 is equal to 0

x times open paren x plus 2 close paren is equal to 24

x squared plus open paren x plus 2 close paren squared is equal to 100

0 point 5 x open paren x plus 2 close paren is equal to 24

x squared plus 2 x minus 48 is equal to 0

What is the range of the function?

all real numbers less than or equal to 4

all real numbers greater than or equal to 4

all real numbers greater than or equal to negative 3

all real numbers less than or equal to negative 3

The function f of x is equal to negative x squared minus 2 x plus 15 is shown on the graph. What are the domain and range of the function?

The domain is start set x such that negative 5 is less than x comma x is less than 3 end set . The range is start set y such that y is less than 16 end set .

The domain is all real numbers. The range is start set y such that y is less than 16 end set .

The domain is all real numbers. The range is start set y such that y is less than or equal to 16 end set .

The domain is start set x such that negative 5 is less than or equal to x comma x is less than or equal to 3 end set . The range is start set y such that y is less than or equal to 16 end set .

Which equation represents x , the side length of the greater square?

x squared plus open paren x minus 2 close paren squared is equal to 10

x squared plus 2 x squared is equal to 10

x squared plus 2 x squared is equal to 100

x squared plus open paren x minus 2 close paren squared is equal to 100

Which describes all of the values for which the graph is negative and increasing?

all real values of x where 1 is less than x comma x is less than 4

all real values of x where negative 2 is less than x comma x is less than 4

all real values of x where x is less than negative 2

all real values of x where x is less than 0

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?

x squared plus 2 x is equal to 42

x squared plus x is equal to 42

x squared plus x plus 42 is equal to 0

x squared plus 2 x plus 42 is equal to 0

Which represents the solution(s) of the graphed system of equations, y is equal to x squared minus 2 x and y is equal to negative 2 x minus 1 ? Open image in full-screen view

1 comma negative 1

0 comma 0 and 0 comma negative 1

0 comma 0 and 2 comma 0

no solutions

A function g of x has x -intercepts at 1 half comma 0 and 6 comma 0 Which could be g of x ?

g of x is equal to open paren x minus 6 close paren times open paren 2 x minus 1 close paren

g of x is equal to 2 open paren x minus 2 close paren open paren x minus 6 close paren

g of x is equal to 2 open paren x plus 1 close paren open paren x plus 6 close paren

g of x is equal to open paren x plus 6 close paren times open paren x plus 2 close paren

What is the first step in solving the quadratic equation negative 5 x squared plus 8 is equal to 133 ?

adding 8 to both sides of the equation

taking the square root of both sides of the equation

squaring both sides of the equation

subtracting 8 from both sides of the equation

Brianna is graphing the function f of x is equal to x squared plus 6 x plus 5 What x -intercepts should Brianna use to graph f of x ?

negative 5 and negative 1

1 and 5

negative 5 and 1

negative 1 and 5

What are the solutions to x squared plus 8 x plus 7 is equal to 0 ?

x is equal to negative 8 and x is equal to negative 7

x is equal to negative 7 and x is equal to negative 1

x is equal to 7 and x is equal to 8

x is equal to 1 and x is equal to 7

What is the vertex of the graph of the function f of x is equal to x squared plus 8 x minus 2 ?

negative 4 comma 18

0 comma negative 2

negative 4 comma negative 18

negative 8 comma negative 2

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?

l times l minus 2 is equal to 168

1 half l squared is equal to 168

2 l squared is equal to 168

l times l plus 2 is equal to 168

The function f of x is equal to negative open paren x minus 3 close paren squared plus 9 can be used to represent the area of a rectangle with a perimeter of 12 units, as a function of the length of the rectangle, x What is the maximum area of the rectangle?

3 square units

9 square units

6 square units

12 square units

What are the solutions of the quadratic equation open paren x plus 3 close paren squared is equal to 49 ?

x is equal to 2 and x is equal to square root of negative 10

x is equal to negative 2 and x is equal to negative 16

x is equal to 4 and x is equal to negative 10

x is equal to 40 and x is equal to negative 58

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

11 by 9

8 by 5

10 by 4

13 by 7

Which represents the solution(s) of the graphed system of equations, y is equal to negative x squared plus x plus 2 and y is equal to negative x plus 3 ? Open image in full-screen view

1 comma 2 and 0 comma 3

1 comma 2

2 comma 1

negative 1 comma 0 and 2 comma 0

Which is the graph of f of x is equal to x squared minus 2 x plus 3 ?

Image with description A coordinate plane with a parabola. The x-axis is labeled from negative 5 to 5 in increments of 1 and the y-axis is labeled from negative 5 to 5 in increments of 1. The parabola opens upward with its vertex at approximately 0 comma 3, on the y-axis. The curve extends symmetrically upward, with the left arm rising into the upper-left area of the plane and the right arm ending near the point 1 comma 5 at the upper-right edge of the visible portion of the curve.

Image with description A coordinate plane with a parabola. The x-axis is labeled from negative 5 to 5 in increments of 1 and the y-axis is labeled from negative 5 to 5 in increments of 1. The parabola opens upward with its vertex at approximately 2 comma 0, on the x-axis. The curve extends symmetrically upward to the left and to the right, with the left arm rising into the upper-left portion of the plane and the right arm rising into the upper-right portion of the plane.

Image with description A coordinate plane with a parabola. The x-axis is labeled from negative 5 to 5 in increments of 1 and the y-axis is labeled from negative 5 to 5 in increments of 1. The parabola opens upward with its vertex at approximately negative 3 comma 2. The curve extends symmetrically upward, with the left arm rising steeply into the upper-left portion of the plane and the right arm visible in the upper-center area near the y-axis.

Image with description A coordinate plane with a parabola. The x-axis is labeled from negative 5 to 5 in increments of 1 and the y-axis is labeled from negative 5 to 5 in increments of 1. The parabola opens upward with its vertex at approximately negative 1 comma 3. The curve extends symmetrically upward, with the left arm rising steeply into the upper-left portion of the plane and the right arm visible near the y-axis in the upper-center area of the plane.

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Quadratic Functions and Equations — Test Answers

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