Answers CMS 2025-2026 Foundations of Math 1 Credit RecoveryModeling with Quadratic Equations

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The tile along the edge of a triangular community pool needs to be replaced.

12x2 + 15

20x2 + 25

12x2 + 8x + 25

24x2 + 16x + 50

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The variables A, B, and C represent polynomials where A = x + 1, B = x2 + 2x − 1, and C = 2x. What is AB + C in simplest form?

x3 + 3x − 1

x3 + 4x − 1

x3 + 3x2 + 3x − 1

x3 + 2x2 − x + 1

What is the difference of the polynomials?(5x3 + 4x2) – (6x2 – 2x – 9)

–x3 + 6x2 + 9

–x3 + 2x2 – 9

5x3 – 2x2 – 2x – 9

5x3 – 2x2 + 2x + 9

A square piece of paper has an area of x2 square units. A rectangular strip with a width of 2 units and a length of x units is cut off of the square piece of paper. The remaining piece of paper has an area of 120 square units.

x2 − 2x − 120 = 0

x2 + 2x − 120 = 0

x2 − 2x + 120 = 0

x2 + 2x + 120 = 0

Which is the simplified form of the expression ?

StartFraction 1 Over 2 Superscript 36 Baseline 3 Superscript 48 Baseline EndFraction

StartFraction 1 Over 3 Superscript 8 Baseline EndFraction

3 Superscript 8

2 Superscript 36 Baseline 3 Superscript 48

Half of the product of two consecutive numbers is 105. Which equation can be used to solve for n, the smaller of the two numbers?

n2 + n – 210 = 0

n2 + n – 105 = 0

2n2 + 2n + 210 = 0

2n2 + 2n + 105 = 0

Which graph represents the function y = 2x – 4?

Option

The table shows the total cost of purchasing x same-priced items and a catalog.

$4, the cost per item

$4, the cost of the catalog

$6, the cost per item

$6, the cost of the catalog

Gerri purchases a coupon book with discounts for her favorite coffee shop. Every coupon for the coffee shop offers the same discount. The table shows her total savings, y, based on the number of coupons, x, used from the book.

slope: 2, y-intercept: –20

slope: 2, y-intercept: 10

slope: 5, y-intercept: –20

slope: 5, y-intercept: 10

Line ST and point V are shown on the graph.

−7

−5

Which function has real zeros at x = –8 and x = 5?

g(x) = x2 + 3x – 40

g(x) = x2 + 3x + 40

g(x) = x2 + 14x – 40

g(x) = x2 + 14x + 40

Which is the value of this expression when and ?

Negative one-third

Negative StartFraction 1 Over 27 EndFraction

StartFraction 1 Over 27 EndFraction

One-third

Arturo is building a flower bed in the shape of a right triangle. The hypotenuse of the right triangle is 13 feet. One of the legs needs to be 7 feet longer than the other leg.

x(x + 7) = 13

x(x + 7) = 169

x2 + (x + 7)2 = 13

x2 + (x + 7)2 = 169

Which term can be added to the list so that the greatest common factor of the three terms is 12h3?36h3, 12h6, __________

6h3

12h2

30h4

48h5

Wren recorded an outside temperature of –2°F at 8 a.m. When she checked the temperature again, it was 4°F at 12:00 p.m. If x represents the time and y represents the temperature in degrees Fahrenheit, what is the slope of the line through these two data points?

–1.5

–0.5

0.5

1.5

Point E is drawn on the graph so that line EF is parallel to line CD.

−8

−4

What are the values of a and b in the equation ?

a = 2, b = 4

a = negative 2, b = 4

a = negative 2, b = negative 4

a = 2, b = negative 4

The graph of y = x2 + 11x + 24 is equivalent to the graph of which equation?

y = (x + 8)(x + 3)

y = (x + 4)(x + 6)

y = (x + 9)(x + 2)

y = (x + 7)(x + 4)

Simplify the expression –3(x + 3)2 – 3 + 3x. What is the simplified expression in standard form?

–3x2 – 18x – 27

–3x2 – 15x – 30

–3x2 + 3x + 6

–3x2 + 3x – 30

A team is selling discount cards as a fundraiser. The table shows the number of cards sold and the remaining amount of money needed.

zero

undefined

negative

positive

Which expression is equivalent to 7a2b + 10a2b2 + 14a2b3?

ab(7a2 + 10ab + 14b2)

a2b(7 + 10b + 14b2)

7a2(b + 3b2 + 7b3)

7a2b3(b2 + 3b + 7)

The equation x2 – 1x – 90 = 0 has solutions {a, b}. What is a + b?

–19

–9

Which can be used to describe an equivalent expression for ?

Adding the exponents will create an equivalent expression.

Dividing the exponents will create an equivalent expression.

There are three factors of .

Which expression is a difference of squares with a factor of 5x − 8?

25x2 − 16

25x2 + 16

25x2 − 64

25x2 + 64

Which is the simplified form of ?

StartFraction 1 Over m Superscript 8 Baseline p EndFraction

StartFraction 1 Over m Superscript 8 EndFraction

StartFraction p over m Superscript 8 EndFraction

m Superscript 8

Which is the graph of f(x) = (x + 3)(x – 2)?

Option

What is the midpoint of the x-intercepts off(x) = (x – 4)(x + 4)?

(0,0)

(0,4)

(–4,0)

(2,0)

Which expression is equivalent to –6x3 • x • y2 • y6?

mc010-1.jpg

mc010-2.jpg

mc010-3.jpg

mc010-4.jpg

What is the coefficient of x after simplifying (−x−5)2?

−25

−10

A perfect square trinomial can be represented by a square model with equivalent length and width. Which polynomial can be represented by a perfect square model?

x2 – 6x + 9

x2 – 2x + 4

x2 + 5x + 10

x2 + 4x + 16

A tree company charges a delivery fee for each tree purchased in addition to the cost of the tree. The delivery fee decreases as the number of trees purchased increases. The table below represents the total cost of x trees purchased, including delivery fees.

The rate of change between 1 and 2 trees is different than the rate of change between 2 and 3 trees.

The rate of change between 1 and 2 trees is different than the rate of change between 1 and 3 trees.

The rate of change between 2 and 3 trees is different than the rate of change between 3 and 4 trees.

The rate of change between 2 and 3 trees is different than the rate of change between 3 and 5 trees.

What is the value of ?

Negative StartFraction 81 Over 16 EndFraction

Negative StartFraction 16 Over 81 EndFraction

StartFraction 16 Over 81 EndFraction

StartFraction 81 Over 16 EndFraction

Consider the quadratic function. f(p) = p2 – 8p – 5What are the values of the coefficients and the constant in the function?

a = –1, b = –8, c = –5

a = 1, b = –5, c = –8

a = 1, b = –8, c = –5

a = –1, b = –5, c = 8

Which expression is equivalent to ?

mc019-2.jpg

mc019-3.jpg

mc019-4.jpg

mc019-5.jpg

The graph of which function has a minimum located at (4, –3)?

f(x) = x2 + 4x – 11

f(x) = –2x2 + 16x – 35

f(x) = x2 – 4x + 5

f(x) = 2x2 – 16x + 35

Which graph shows a rate of change of between –4 and 0 on the x-axis?

On a coordinate plane, a straight line with a positive slope crosses the x-axis at (6, 0) and the y-axis at (0, 3). Solid circles appear on the line at (negative 4, negative 1), (0, 3).

On a coordinate plane, a parabola opens up. It goes through (negative 5.25, 4), has a vertex of (0, negative 3), and goes through (5.25, 4). Solid circles appear on the parabola at (negative 4, 1), (0, negative 3).

On a coordinate plane, a parabola opens down. It goes through (negative 5.5, negative 4), has a vertex of (0, 4), and goes through (5.5, negative 4). Solid circles appear on the parabola at (negative 4, 0), (0, 4).

On a coordinate plane, a curved line opens up and left in quadrant 2. It is asymptotic to the negative x-axis and positive y-axis. Solid circles appear on the line at (negative 4, 0.25), (0, 4).

A rectangle with an area of x2 – 4x – 12 square units is represented by the model.

(x + 2) and (x – 6)

(x + 6) and (x – 2)

(x + 2) and (x – 10)

(x + 10) and (x – 2)

What is the product?

24 a squared minus 6 b

24 a squared minus 6 a b

24 a squared minus 18 b squared

24 a squared minus 18 a b

What is the factored form of x2 – 6x – 16?

(x – 4)(x – 2)

(x + 4)(x – 2)

(x – 2)(x + 8)

(x – 8)(x + 2)

The monomial 36x4 is a perfect square. What is the square root of 36x4?

6x2

6x4

18x2

18x4

The graph of which function has an axis of symmetry at x = ?

f(x) = 2x2 + x – 1

f(x) = 2x2 – x + 1

f(x) = x2 + 2x – 1

f(x) = x2 – 2x + 1

The diagram represents the polynomial 4x2 + 23x – 72.

(4x + 8)(x – 9)

(4x – 8)(x + 9)

(4x + 9)(x – 8)

(4x – 9)(x + 8)

What are the factors of 2x2 + 3x – 54? Select two options.2x – 92x – 62x + 6x – 6x + 6

2x – 9

2x – 6

2x + 6

x – 6

x + 6

The projectile motion of an object can be modeled using s(t) = gt2 + v0t + s0, where g is the acceleration due to gravity, t is the time in seconds since launch, s(t) is the height after t seconds, v0 is the initial velocity, and s0 is the initial height. The acceleration due to gravity is –4.9 m/s2.

0 = –4.9t2 + 19.6t + 24.5

0 = –4.9t2 + 24.5t + 19.6

19.6 = –4.9t2 + 24.5t

24.5 = –4.9t2 + 19.6t

The product of a binomial and a trinomial is x 3 + 3 x 2 − x + 2 x 2 + 6 x − 2. Which expression is equivalent to this product after it has been fully simplified?

x3 + 5x2 + 5x – 2

x3 + 2x2 + 8x – 2

x3 + 11x2 – 2

x3 + 10x2 – 2

Blake knows that one of the solutions to x2 – 6x + 8 = 0 is x = 2. What is the other solution?

x = –6

x = –3

x = 4

x = 8

The projectile motion of an object can be modeled usings(t) = gt2 + v0t + s0, where g is the acceleration due to gravity, t is the time in seconds since launch, s(t) is the height after t seconds, v0 is the initial velocity, and s0 is the initial height. The acceleration due to gravity is –4.9 m/s2.

s(t) = –4.9t2 + 39.2

s(t) = –4.9t2 + 39.2t

s(t) = –4.9t2 + 39.2t + 39.2

s(t) = –4.9t2 + 39.2t – 39.2

Megan and Suzanne each have a plant. They track the growth of their plants for four weeks. Whose plant grew at a faster rate, and what was the rate?