Factoring Quadratics

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 expressing 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

What are the roots of a quadratic equation?

Back

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

Front

How do you solve a quadratic equation by taking square roots?

Back

To solve by taking square roots, isolate the x² term, then take the square root of both sides, remembering to consider both the positive and negative roots.

Front

What is the vertex of a parabola?

Back

The vertex of a parabola is the highest or lowest point on the graph, depending on whether it opens upwards or downwards.

Front

What does it mean if a parabola opens upwards?

Back

If a parabola opens upwards, it has a minimum vertex, and the y-values increase as you move away from the vertex.

Front

What does it mean if a parabola opens downwards?

Back

If a parabola opens downwards, it has a maximum vertex, and the y-values decrease as you move away from the vertex.

Front

How can you determine the direction a parabola opens?

Back

The direction a parabola opens can be determined by the sign of the leading coefficient (a) in the quadratic equation ax² + bx + c. If a > 0, it opens upwards; if a < 0, it opens downwards.

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 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.