another math test

Which represents the solution(s) of the system of equations, y = x2 - 6x + 8 and y = -x + 4? Determine the solution set by graphing.

(1, 3) and (4, 0)

Solve x2 = 12x - 15 by completing the square. Which is the solution set of the equation?

(6-21,6+21)

Brianna is graphing the function f(x) = x2 + 6x + 5. What x-intercepts should Brianna use to graph f(x)?

-5 and -1

The area of the right triangle shown is 24 square feet. Which equations can be used to find the lengths of the legs of the triangle? Select three options.

0.5(x)(x + 2) = 24 x2 + 2x - 48 = 0 x2 + (x + 2)2 = 100

Rounded to the nearest hundredth, what is the positive solution to the quadratic equation 0=2x2+3x-8?

1.39

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?

10 by 4

What number should be added to both sides of the equation to complete the square? x2 - 10x = 7

25

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

36

A rectangle's length is three times its width, w. Its area is 243 square units. Which equation can be used to find the width of the rectangle?

3w2 = 243

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 +

81

Solve x2 - 8x = 3 by completing the square. Which is the solution set of the equation?

A

What are the zeros of the function f(x) = x2 + 5x + 5 written in simplest radical form?

C

Which shows the correct substitution of the values a, b, and c from the equation -2 = -x + x2 - 4 into the quadratic formula?

D

Zacharias is using the quadratic formula to solve the equation 0 = -2x2 + 5x - 3. He begins by substituting as shown. Quadratic formula: x = Substitution: x = What error did Zacharias make?

The 2 in the numerator should be -2.

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

a = -4, b = 5, c = -2

Alessandro wrote the quadratic equation -6=x2+4x-1 in standard form. What is the value of c in his new equation?

c=5

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

g(x) = (x - 6)(2x - 1)

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(l - 2) = 168

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

no solutions

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

q = 5 q = -5

What are the solutions to x2 + 8x + 7 = 0?

x = -7 and x = -1

What are the solutions of the quadratic equation (x + 3)2 = 49?

x = 4 and x = -10

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?

x2 + x = 42

Which equations are true for x = -2 and x = 2? Select two options

x2 - 4 = 0 4x2 = 16

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

x= 5/2-31/2 and x= 5/2+31/2