Bluebook SAT Test Nonlinear Equations and Systems 10

Question 1

A rocket's height in feet is h(t) = −16t² + 80t. What is the maximum height the rocket reaches?

Accepted Answer

100 feet

Answer

Vertex time: t = −80/(2 × −16) = 2.5 s; h(2.5) = −16(6.25) + 80(2.5) = −100 + 200 = 100 feet.

Question 2

How many solutions does the system y = x² − 2x + 1 and y = 4 have?

Accepted Answer

2 solutions

Answer

x² − 2x + 1 = 4 → x² − 2x − 3 = 0 → (x − 3)(x + 1) = 0; two solutions: x = 3 and x = −1.

Question 3

The equation x² − kx + 9 = 0 has two equal real roots. What is the positive value of k?

Accepted Answer

6

Answer

For equal roots, discriminant = 0: k² − 36 = 0; k² = 36; k = 6.

Question 4

Which value of x satisfies both x² = 2x + 8 and x > 0?

Accepted Answer

x = 4

Answer

x² − 2x − 8 = 0 → (x − 4)(x + 2) = 0; the positive solution is x = 4.

Question 5

The graph of y = −(x − 3)² + 5 has its vertex at which point?

Accepted Answer

(3, 5)

Answer

In vertex form y = a(x − h)² + k, the vertex is (h, k) = (3, 5).

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