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The first few steps in deriving the quadratic formula are shown.

The term is added to the right side of the equation, so it needs to be subtracted from the left side of the equation to balance the sides of the equation.

The distributive property needs to be applied to determine the value to add to the left side of the equation to balance the sides of the equation.

The term needs to be converted so it has a common denominator before adding it to the left side of the equation to balance the equation.

The square root of the term needs to be found before adding the term to the left side of the equation to balance the sides of the equation.

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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

Given the function f(x) = 3|x – 2| + 6, for what values of x is f(x) = 18?

x = –2, x = –8

x = –2, x = –6

x = –2, x = 6

x = –2, x = 8

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

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

Option

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

What does a residual value of 1.3 mean when referring to the line of best fit of a data set?

A data point is 1.3 units above the line of best fit.

A data point is 1.3 units below the line of best fit.

The line of best fit has a slope of –1.3

The line of best fit has a slope of 1.3.

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

25x2 − 16

25x2 + 16

25x2 − 64

25x2 + 64

Which is the solution of the quadratic equation (4y – 3)2 = 72?

y = and y =

y = and y =

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

ab(7a2 + 10ab + 14b2)

a2b(7 + 10b + 14b2)

7a2(b + 3b2 + 7b3)

7a2b3(b2 + 3b + 7)

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 table shows no correlation?

A 2-row table with 7 columns. The first row is labeled x with entries 3, 5, 6, 8, 10, 14, 15. The second row is labeled y with entries negative 1, negative 2, negative 3, negative 2, negative 5, negative 4, negative 8.

A 2-row table with 7 columns. The first row is labeled x with entries 3, 5, 6, 8, 10, 14, 15. The second row is labeled y with entries negative 6, negative 7, negative 4, negative 2, 0, negative 1, positive 3.

A 2-row table with 7 columns. The first row is labeled x with entries 3, 5, 6, 8, 10, 14, 15. The second row is labeled y with entries negative 2, negative 4, positive 6, positive 8, positive 12, positive 10, negative 16.

A 2-row table with 7 columns. The first row is labeled x with entries 3, 5, 6, 8, 10, 14, 15. The second row is labeled y with entries negative 3, negative 5, negative 9, negative 11, negative 13, negative 15, negative 17.

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 equation has an a-value of 1, a b-value of –3, and a c-value of –5?

0 = –3x – 5 + x2

0 = x – 3 – 5x2

0 = 3x – 5 – x2

0 = –3x + 5 – x2

Solve x2 + 10x = 24 by completing the square. Which is the solution set of the equation?

(negative 5 minus StartRoot 34 EndRoot comma negative 5 + Startroot 34 EndRoot)

(negative 5 minus StartRoot 29 EndRoot comma negative 5 + StartRoot 29 EndRoot)

{–12, 2}

{–2, 12}

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

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

What is f(x) = 7x2 + 42x written in vertex form?

f(x) = 7(x + 6)2 – 6

f(x) = 7(x + 6)2 – 42

f(x) = 7(x + 3)2 – 9

f(x) = 7(x + 3)2 – 63

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

6x2

6x4

18x2

18x4

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

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

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

(4x + 8)(x – 9)

(4x – 8)(x + 9)

(4x + 9)(x – 8)

(4x – 9)(x + 8)

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