Bluebook SAT Test Nonlinear Equations and Systems 12

Question 1

The function g(x) = x² − 4x + 3 is reflected over the x-axis to form h(x). What is h(5)?

Accepted Answer

−8

Answer

h(x) = −g(x) = −(x² − 4x + 3); h(5) = −(25 − 20 + 3) = −8.

Question 2

The parabola y = x² + 2x − 15 is tangent to the horizontal line y = k. What is the value of k?

Accepted Answer

−16

Answer

Vertex y-value = minimum = c − b²/(4a) = −15 − 4/4 = −15 − 1 = −16.

Question 3

Solve for x: (x − 4)² − 9 = 0

Accepted Answer

x = 1 and x = 7

Answer

(x − 4)² = 9 → x − 4 = ±3 → x = 7 or x = 1.

Question 4

For the system y = x² + 1 and y = 5, how many solutions are there?

Accepted Answer

2

Answer

x² + 1 = 5 → x² = 4 → x = ±2; two solutions.

Question 5

The equation 4x² − 4x + 1 = 0 has how many distinct real solutions?

Accepted Answer

1

Answer

Discriminant = (−4)² − 4(4)(1) = 16 − 16 = 0; exactly one real solution (a repeated root).

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