Bluebook SAT Test Nonlinear Equations and Systems 6

Question 1

The product of two numbers is 40 and their sum is 13. Which quadratic equation has these two numbers as roots?

Accepted Answer

x² − 13x + 40 = 0

Answer

x² + 13x + 40 = 0

Answer

x² − 13x − 40 = 0

Answer

x² + 13x − 40 = 0

Question 2

What is the x-coordinate of the axis of symmetry of y = −2x² + 8x − 5?

Accepted Answer

x = 2

Answer

x = −2

Answer

x = 4

Answer

x = −4

Question 3

The system y = 2x + k and y = x² has exactly one solution. What is k?

Accepted Answer

−1

Answer

−2

Answer

1

Answer

2

Question 4

If 5x² = 45, what is the value of x²?

Accepted Answer

9

Answer

3

Answer

5

Answer

15

Question 5

Which of the following best describes the solutions of x² + 2x + 5 = 0?

Accepted Answer

No real solutions

Answer

Two distinct real solutions

Answer

One repeated real solution

Answer

Two equal rational solutions

Question 6

The parabola y = x² − 6x + 5 is shifted 3 units to the right. What is the equation of the new parabola?

Accepted Answer

y = x² − 12x + 32

Answer

y = x² − 9x + 14

Answer

y = x² − 6x + 2

Answer

y = x² − 3x + 2

Question 7

For the equation 2x² + 5x − 3 = 0, what is the product of the roots?

Accepted Answer

−3/2

Answer

5/2

Answer

3/2

Answer

−5/2