Solve Quadratics by Factoring

Front

What is a quadratic equation?

Back

A quadratic equation is a polynomial equation of the form ax² + bx + c = 0, where a, b, and c are constants and a ≠ 0.

Front

What does it mean to factor a quadratic equation?

Back

Factoring a quadratic equation means rewriting it as a product of two binomials, such as (x - p)(x - q) = 0, where p and q are the roots of the equation.

Front

How do you find the roots of a quadratic equation by factoring?

Back

To find the roots, set the factored form of the equation to zero and solve for x.

Front

What is the axis of symmetry in a parabola?

Back

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

Front

What is the vertex of a parabola?

Back

The vertex is the highest or lowest point of the parabola, located at the coordinates (h, k) in the vertex form of a quadratic equation: y = a(x - h)² + k.

Front

Solve the quadratic equation: x² - 7x = 0

Back

x = 0, 7

Front

Solve the quadratic equation: 3x² - 48 = 0

Back

x = -4, 4

Front

Solve the quadratic equation: x² - 14x - 51 = 0

Back

x = 17, -3

Front

What is the standard form of a quadratic equation?

Back

The standard form of a quadratic equation is ax² + bx + c = 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.