Solving Quadratic Equations Flashcards

What is the axis of symmetry of the parabola y = 2x² − 8x + 3?

Answer: x = 2

Axis of symmetry: x = −b/(2a) = 8/4 = 2.

Solve x² − 2x − 8 = 0 using the quadratic formula.

Answer: x = 4 and x = −2

x = (2 ± √36) / 2 = (2 ± 6) / 2, giving x = 4 or x = −2.

If the roots of a quadratic are x = 5 and x = −3, which equation fits?

Answer: x² − 2x − 15 = 0

Sum of roots = 2, product = −15, so the equation is x² − 2x − 15 = 0.

Solve (x − 3)² = 25.

Answer: x = 8 and x = −2

x − 3 = ±5, so x = 8 or x = −2.

Which quadratic equation has roots that are both negative?

Answer: x² + 5x + 6 = 0

x² + 5x + 6 = (x + 2)(x + 3) = 0 gives x = −2 and x = −3, both negative.

A quadratic has the form x² + px + q = 0. If the discriminant is zero, which statement is true?

Answer: The equation has exactly one solution

A zero discriminant means the quadratic is a perfect square with exactly one repeated root.

Solve 6x² − x − 2 = 0 by factoring.

Answer: x = ⅔ and x = −½

Factoring gives (3x − 2)(2x + 1) = 0, so x = ⅔ or x = −½.