Factoring and Solving Quadratic Equations

Front

What is the quadratic formula?

Back

The quadratic formula is x = (-b ± √(b² - 4ac)) / (2a), used to find the solutions of a quadratic equation ax² + bx + c = 0.

Front

What does GCF stand for in factoring?

Back

GCF stands for Greatest Common Factor, which is the largest factor that divides two or more numbers.

Front

How do you factor a quadratic expression of the form ax² + bx + c?

Back

To factor a quadratic expression, find two numbers that multiply to ac and add to b, then rewrite the expression using these numbers.

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

What is the solution set of a quadratic equation?

Back

The solution set of a quadratic equation is the set of values of x that satisfy the equation, often found using factoring or the quadratic formula.

Front

How do you simplify an expression by factoring out the GCF?

Back

To simplify by factoring out the GCF, divide each term by the GCF and write the expression as the GCF multiplied by the simplified expression.

Front

What is the factored form of 25x² - 36?

Back

The factored form of 25x² - 36 is (5x + 6)(5x - 6).

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 and solve for x.

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 significance of the discriminant in a quadratic equation?

Back

The discriminant (b² - 4ac) determines the nature of the roots: if positive, two real roots; if zero, one real root; if negative, no real roots.