Bluebook SAT Test Nonlinear Equations and Systems 11

Question 1

For the quadratic f(x) = 2x² − 8x + 6, what are the x-intercepts?

Accepted Answer

x = 1 and x = 3

Answer

2x² − 8x + 6 = 2(x² − 4x + 3) = 2(x − 1)(x − 3); x-intercepts at x = 1 and x = 3.

Question 2

Solve: x² − 81 = 0

Accepted Answer

x = ±9

Answer

x² = 81; x = ±9.

Question 3

The system y = 2x − 1 and y = x² − 4x + 3 is solved. What is the product of the x-coordinates of the solutions?

Accepted Answer

4

Answer

2x − 1 = x² − 4x + 3 → x² − 6x + 4 = 0; by Vieta's, product of roots = c/a = 4.

Question 4

A quadratic has a positive leading coefficient and vertex at (2, −3). How many x-intercepts does it have?

Accepted Answer

2

Answer

The parabola opens upward (positive leading coefficient) and its minimum is −3 < 0; it must cross the x-axis twice.

Question 5

If x² + 12x + c = (x + 6)², what is the value of c?

Accepted Answer

36

Answer

(x + 6)² = x² + 12x + 36, so c = 36.

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