Bluebook SAT Test Nonlinear Equations and Systems 15

Question 1

Which of the following is a solution to x² − x − 6 > 0?

Accepted Answer

x = 4

Answer

x² − x − 6 = (x − 3)(x + 2); this is > 0 when x > 3 or x < −2; x = 4 satisfies x > 3.

Question 2

What is the axis of symmetry for y = 3x² + 18x + 7?

Accepted Answer

x = −3

Answer

Axis of symmetry: x = −b/(2a) = −18/6 = −3.

Question 3

The sum of a positive integer and its square is 42. What is the integer?

Accepted Answer

6

Answer

n + n² = 42 → n² + n − 42 = 0 → (n + 7)(n − 6) = 0; positive solution is n = 6.

Question 4

The revenue from selling x units is R(x) = −2x² + 40x. What number of units maximizes revenue?

Accepted Answer

10 units

Answer

Maximum at vertex: x = −40/(2 × −2) = −40/−4 = 10 units.

Question 5

Which of the following is equivalent to x² − 6x + 8?

Accepted Answer

(x − 2)(x − 4)

Answer

(x − 2)(x − 4) = x² − 6x + 8. ✓

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