Retake Retake Unit 2 Flashcard 3 Part A

Front

What is the quadratic formula?

Back

The quadratic formula is used to find the solutions of a quadratic equation in the form ax^2 + bx + c = 0. It is given by x = (-b ± √(b² - 4ac)) / (2a).

Front

How do you solve a quadratic equation by factoring?

Back

To solve a quadratic equation by factoring, express the equation in the form (px + q)(rx + s) = 0, then set each factor to zero and solve for x.

Front

What is the discriminant in a quadratic equation?

Back

The discriminant is the part of the quadratic formula under the square root, given by b² - 4ac. It determines the nature of the roots: if positive, there are two real roots; if zero, one real root; if negative, two complex roots.

Front

Solve for x: 2x^2 - 10x + 11 = 0

Back

x = (5 + √3) / 2, x = (5 - √3) / 2.

Front

Solve for x by factoring: 4x^2 + 5 = 6

Back

x = ± 1/2.

Front

Solve for x by factoring: x^2 + 10x = 24

Back

x = {-12, 2}.

Front

What is the standard form of a quadratic equation?

Back

The standard form of a quadratic equation is ax^2 + bx + c = 0, where a, b, and c are constants and a ≠ 0.

Front

Solve for x using the quadratic formula: x^2 - 6x - 23 = 0

Back

x = 3 ± 4√2.

Front

Solve for x by factoring: 5x^2 + 14x = x + 6

Back

x = -3, 2/5.

Front

What is the vertex form of a quadratic function?

Back

The vertex form of a quadratic function is y = a(x - h)² + k, where (h, k) is the vertex of the parabola.