Bluebook SAT Test Nonlinear Equations and Systems 4

Question 1

The sum of a number and its square is 56. Which equation models this situation?

Accepted Answer

x² + x − 56 = 0

Answer

Let the number be x; x + x² = 56 rearranges to x² + x − 56 = 0.

Question 2

For the equation 4x² − 20x + 25 = 0, how many real solutions are there?

Accepted Answer

1

Answer

Discriminant = (−20)² − 4(4)(25) = 400 − 400 = 0, so exactly one repeated real solution.

Question 3

What is the solution set of x² − 9 = 0?

Accepted Answer

{3, −3}

Answer

x² = 9 → x = ±3.

Question 4

The system y = x² − 2x − 3 and y = 5 is solved. What are the x-values of the intersections?

Accepted Answer

x = 4 and x = −2

Answer

x² − 2x − 3 = 5 → x² − 2x − 8 = 0 → (x−4)(x+2) = 0 → x = 4 or x = −2.

Question 5

A ball is thrown upward; its height in feet at time t seconds is h(t) = −16t² + 64t. At what time does the ball return to the ground (h = 0, t > 0)?

Accepted Answer

t = 4 s

Answer

−16t² + 64t = 0 → −16t(t−4) = 0 → t = 0 or t = 4; the ball returns at t = 4 s.

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