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Two numbers are 10 units away in different directions from their midpoint, m, on a number line. The product of the numbers is –99.

(m – 5)(m + 5) = 99

(m – 10)(m + 10) = 99

m2 – 25 = –99

m2 – 100 = –99

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The graph of an exponential function and a linear function are shown below. Exponential Linear Which statement is true about the functions?

The exponential function is generally growing slower than the linear function.

The exponential function is generally growing faster than the linear function.

The linear function is generally growing faster than the exponential function.

The exponential function and the linear function are generally growing at the same rate.

Solve x2 + 6x = 7 by completing the square. Which is the solution set of the equation?

{–7, 1}

(negative 3 minus StartRoot 10 EndRoot comma negative 3 + StartRoot 10 EndRoot)

(3 minus StartRoot 10 EndRoot comma negative 3 + StartRoot 10 EndRoot)

{1, 7}

Solve x2 – 8x = 20 by completing the square. Which is the solution set of the equation?

{–22, 14}

{–14, 22}

{–10, 2}

{–2, 10}

Sergey is solving 5x2 + 20x – 7 = 0. Which steps could he use to solve the quadratic equation by completing the square? Select three options.5(x2 + 4x + 4) = –7 + 20x + 2 = 5(x2 + 4x) = 75(x2 + 4x + 4) = 7 + 205(x2 + 4x) = –7

5(x2 + 4x + 4) = –7 + 20

x + 2 =

5(x2 + 4x) = 7

5(x2 + 4x + 4) = 7 + 20

5(x2 + 4x) = –7

Fiona is completing the square to solve the polynomial equation.x2 – 4x + 1 = 0

isolating the constant 1

adding 4 to both sides of the equation

isolating the second term, –4x

adding 1 to both sides of the equation

Solve x2 − 24x = −80 by completing the square.What is the solution set of the equation?

{2, 40}

{4, 20}

{5, 16}

{8, 10}

The first few steps in solving the quadratic equation 5x2 + 27x = 14 − 13x by completing the square are shown.5x2 + 27x = 14 − 13x5x2 + 40x = 145(x2 + 8x) = 14

5(x2 + 8x + 16) = 30

5(x2 + 8x + 16) = 94

5(x2 + 8x + 4) = 18

5(x2 + 8x + 4) = 34

Using the Completing the Square method, what are the zeros of the quadratic function f(x) = 2x2 + 8x – 3?

x = –2 – and x = –2 +

x = –2 – and x = –2 +

x = 2 – and x = 2 +

Which is a solution to the equation?(x − 3)(x − 5) = 35

x = −8

x = −5

x = 2

x = 10

Mariya is solving the quadratic equation by completing the square.4x2-20x+3=04x2-20x=-3A(x2-5x)=-3

-20

Between which two ordered pairs does the graph of f(x) = x2 + x – 9 cross the negative x-axis?Quadratic formula: x =

(–6, 0) and (–5, 0)

(–4, 0) and (–3, 0)

(–3, 0) and (–2, 0)

(–2, 0) and (–1, 0)

A quadratic equation of the form 0 = ax2 + bx + c has one real number solution. Which could be the equation?

0 = 2x2 – 4x + 1

0 = 2x2 – 5x + 3

0 = –2x2 – 4x – 2

0 = –2x2 – 3x – 1

Clara writes the equation (x – 13)(x + 8) = 196 to solve for the missing side length of a rectangle represented by the factor x + 8. What is the missing side length represented by x + 8 units of the rectangle?

What is a solution to (x + 6)(x + 2) = 60?

x = −6

x = −4

x = 4

x = 12

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