Bluebook SAT Test Nonlinear Equations and Systems 8

Question 1

Which of the following is a factor of x² + 7x + 12?

Accepted Answer

(x + 3)

Answer

(x − 3)

Answer

(x + 6)

Answer

(x − 4)

Question 2

The line y = −3x + 5 and the parabola y = x² − 4 intersect at two points. What is the product of the x-coordinates of these two points?

Accepted Answer

−9

Answer

−3

Answer

3

Answer

9

Question 3

What is the maximum value of the function f(x) = −x² + 4x + 1?

Accepted Answer

5

Answer

4

Answer

6

Answer

7

Question 4

The equation kx² − 6x + 1 = 0 has two distinct real solutions. Which of the following must be true?

Accepted Answer

k < 9

Answer

k > 9

Answer

k = 9

Answer

k ≥ 9

Question 5

The roots of ax² + bx + c = 0 are both negative. If a > 0, which of the following must be true?

Accepted Answer

b > 0 and c > 0

Answer

b < 0 and c > 0

Answer

b > 0 and c < 0

Answer

b < 0 and c < 0

Question 6

What is the y-intercept of the parabola y = 2x² − 5x + 3?

Accepted Answer

y = 3

Answer

y = −3

Answer

y = 0

Answer

y = 5

Question 7

Solve the system y = x + 2 and y = x² by substitution. What are the x-values of the solutions?

Accepted Answer

x = 2 and x = −1

Answer

x = 0 and x = 2

Answer

x = −2 and x = 1

Answer

x = 1 and x = −2