SAT Math: Quadratics (Drill 3)

Question 1. What are the solutions to 2x² − 7x + 3 = 0?

• A) x = 3 and x = 1/2 ✓
• B) x = −3 and x = −1/2
• C) x = 3 and x = −1/2
• D) x = 7 and x = 3

Explanation: Factor: (2x − 1)(x − 3) = 0. So x = 1/2 or x = 3.

Question 2. A ball is thrown upward with height h(t) = −16t² + 64t + 5, where t is seconds. What is the maximum height?

• A) 64 feet
• B) 69 feet ✓
• C) 128 feet
• D) 5 feet

Explanation: Vertex at t = −b/(2a) = −64/(−32) = 2. h(2) = −16(4) + 64(2) + 5 = −64 + 128 + 5 = 69.

Question 3. Which equation has a vertex at (2, −3)?

• A) y = (x + 2)² − 3
• B) y = (x − 2)² + 3
• C) y = (x − 2)² − 3 ✓
• D) y = (x + 2)² + 3

Explanation: Vertex form is y = a(x − h)² + k. With vertex (2, −3): y = (x − 2)² − 3.

Question 4. For the equation x² + 4x + k = 0, what value of k gives exactly two distinct real solutions?

• A) 4
• B) 5
• C) 3 ✓
• D) 8

Explanation: Discriminant = b² − 4ac = 16 − 4k > 0 for two real solutions. 16 − 4k > 0 means k < 4. Only k = 3 satisfies this among the choices.

Question 5. The graph of y = x² − 6x + 8 crosses the x-axis at which points?

• A) (2, 0) and (4, 0) ✓
• B) (−2, 0) and (−4, 0)
• C) (3, 0) and (8, 0)
• D) (1, 0) and (8, 0)

Explanation: Factor: x² − 6x + 8 = (x − 2)(x − 4) = 0. x-intercepts at x = 2 and x = 4.