Nonlinear Equations and Systems Flashcards

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

Answer: x = 4

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

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

Answer: x = −3

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

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

Answer: 6

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

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

Answer: 10 units

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

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

Answer: (x − 2)(x − 4)

(x − 2)(x − 4) = x² − 6x + 8. ✓

For the equation x² + 5x = 14, what are both solutions?

Answer: x = −7 and x = 2

x² + 5x − 14 = 0 → (x + 7)(x − 2) = 0; x = −7 or x = 2.

The parabola y = (x + 4)(x − 2) intersects the y-axis at which point?

Answer: (0, −8)

At x = 0: y = (4)(−2) = −8; y-intercept is (0, −8).