Factoring and Solving Quadratic Equations

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 and a ≠ 0.

Front

What does it mean to 'complete the square'?

Back

Completing the square is a method used to convert a quadratic equation into a perfect square trinomial, making it easier to solve.

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

How do you factor a quadratic expression?

Back

To factor a quadratic expression, find two numbers that multiply to ac (the product of a and c) and add to b (the coefficient of x).

Front

What is the GCF (Greatest Common Factor)?

Back

The GCF is the largest factor that divides two or more numbers or expressions.

Front

What is the factored form of a difference of squares?

Back

The factored form of a difference of squares a² - b² is (a + b)(a - b).

Front

How do you solve a quadratic equation by factoring?

Back

To solve by factoring, rewrite the equation in the form (x - p)(x - q) = 0, then set each factor to zero: x - p = 0 or x - q = 0.

Front

What is a perfect square trinomial?

Back

A perfect square trinomial is an expression of the form a² ± 2ab + b², which factors to (a ± b)².

Front

What is the vertex form of a quadratic equation?

Back

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

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. It determines the nature of the roots.