Bluebook SAT Test Nonlinear Equations and Systems 5

Question 1

Using the quadratic formula, what are the solutions to 2x² − 4x − 6 = 0?

Accepted Answer

x = 3 and x = −1

Answer

Divide by 2: x² − 2x − 3 = 0 → (x−3)(x+1) = 0 → x = 3 or x = −1.

Question 2

The parabola y = (x − 3)² − 4 intersects the x-axis at which two values of x?

Accepted Answer

x = 1 and x = 5

Answer

Set y = 0: (x−3)² = 4 → x−3 = ±2 → x = 5 or x = 1.

Question 3

How many solutions does the system y = x² + 3x + 2 and y = x + 2 have?

Accepted Answer

2

Answer

x² + 3x + 2 = x + 2 → x² + 2x = 0 → x(x+2) = 0 → x = 0 or x = −2; two solutions.

Question 4

The equation x² + px + 16 = 0 has two equal real roots. What is the positive value of p?

Accepted Answer

8

Answer

Equal roots require discriminant = 0: p² − 64 = 0 → p = ±8; the positive value is 8.

Question 5

A parabola y = x² − 4x + c does not intersect the x-axis. Which value of c satisfies this condition?

Accepted Answer

c = 5

Answer

Discriminant < 0: 16 − 4c < 0 → c > 4; only c = 5 satisfies this.

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