Factoring Quadratic Equations

Front

What are the zeros of a quadratic equation?

Back

The zeros (or roots) of a quadratic equation are the values of x that make the equation equal to zero.

Front

How do you factor a quadratic equation?

Back

To factor a quadratic equation in the form ax² + bx + c, find two numbers that multiply to ac and add to b, then rewrite the equation as (x + p)(x + q) = 0.

Front

What is the quadratic formula?

Back

The quadratic formula is x = (-b ± √(b² - 4ac)) / (2a), used to find the roots of a quadratic equation.

Front

What does it mean to solve by factoring?

Back

Solving by factoring involves rewriting the quadratic equation as a product of its factors and then setting each factor equal to zero.

Front

What is the vertex of a quadratic function?

Back

The vertex is the highest or lowest point of the parabola represented by the quadratic function.

Front

What is the axis of symmetry in a quadratic equation?

Back

The axis of symmetry is a vertical line that divides the parabola into two mirror-image halves, given by the formula x = -b/(2a).

Front

What are the roots of the equation 2x² - 3x - 2 = 0?

Back

The roots are x = -1/2 and x = 2.

Front

How do you find the roots of the equation (x + 2)(x - 3) = 0?

Back

Set each factor equal to zero: x + 2 = 0 (x = -2) and x - 3 = 0 (x = 3). The roots are -2 and 3.

Front

What is the standard form of a quadratic equation?

Back

The standard form of a quadratic equation is ax² + bx + c = 0, where a, b, and c are constants.

Front

What is the discriminant in a quadratic equation?

Back

The discriminant is the part of the quadratic formula under the square root, b² - 4ac, which determines the nature of the roots.