Drill 1 · Math · Quadratics
SAT Math: Quadratics (Drill 1) is a Math practice drill covering Quadratics. It contains 5 original questions created by Brian Stewart, a Barron's test prep author with over 20 years of tutoring experience.
SAT quadratic questions ask you to factor expressions, apply the quadratic formula, complete the square, find the vertex of a parabola, and interpret what the roots and vertex represent in context. This drill covers all three main forms: standard, factored, and vertex.
Question 1. What is the sum of the solutions to x² + 5x + 6 = 0?
Explanation: Factor: (x + 2)(x + 3) = 0. Solutions are x = −2 and x = −3. Sum = −2 + (−3) = −5. By Vieta's formulas, the sum of roots = −b/a = −5/1 = −5.
Question 2. The function f(x) = (x − 3)² − 4 represents a parabola. What is the minimum value of f(x)?
Explanation: The function is in vertex form: f(x) = (x − 3)² − 4. The vertex is at (3, −4). Since the coefficient of the squared term is positive, the parabola opens upward, so the minimum value is −4.
Question 3. What is the product of the solutions to 2x² − 12x + 10 = 0?
Explanation: Divide by 2: x² − 6x + 5 = 0. Factor: (x − 1)(x − 5) = 0. Solutions are x = 1 and x = 5. Product = 1 × 5 = 5. By Vieta's formulas, product = c/a = 5/1 = 5.
Question 4. How many real solutions does the equation x² + 4x + 5 = 0 have?
Explanation: Discriminant = b² − 4ac = 16 − 20 = −4. Since the discriminant is negative, there are no real solutions.
Question 5. A ball is launched upward from the top of a building. Its height h, in feet, after t seconds is given by h(t) = −16t² + 64t + 80. What is the maximum height, in feet, that the ball reaches?
Explanation: The vertex time is t = −b/(2a) = −64/(−32) = 2 seconds. h(2) = −16(4) + 64(2) + 80 = −64 + 128 + 80 = 144 feet.