Bluebook SAT Test Nonlinear Equations and Systems 7

Question 1

A quadratic equation has roots x = 2 + √3 and x = 2 − √3. What is the quadratic equation?

Accepted Answer

x² − 4x + 1 = 0

Answer

x² + 4x + 1 = 0

Answer

x² − 4x − 1 = 0

Answer

x² + 4x − 1 = 0

Question 2

The height of a projectile is modeled by h = −5t² + 20t + 60. At what positive time t does the projectile hit the ground (h = 0)?

Accepted Answer

t = 6 only

Answer

t = 2 only

Answer

t = −2 and t = 6

Answer

t = 2 and t = −6

Question 3

If 2x² − 8 = 0, what are the solutions for x?

Accepted Answer

x = ±2

Answer

x = ±4

Answer

x = ±2√2

Answer

x = ±√2

Question 4

The system y = x² − x − 6 and y = 2 is solved. What is the sum of the x-coordinates of the intersection points?

Accepted Answer

1

Answer

2

Answer

3

Answer

4

Question 5

What value of c makes x² + 10x + c a perfect square trinomial?

Accepted Answer

25

Answer

20

Answer

30

Answer

100

Question 6

For the system y = x² − 1 and y = 3x − 3, at which x-values do the graphs intersect?

Accepted Answer

x = 1 and x = 2

Answer

x = 2 and x = −1

Answer

x = 1 only

Answer

x = 3 and x = −1

Question 7

The quadratic y = −x² + 6x − 5 has a maximum value. What is that maximum value?

Accepted Answer

4

Answer

3

Answer

5

Answer

6