Solve Quadratic Equations 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.

Front

What is the first step in solving the equation x² + 6x - 13 = 3?

Back

Make it equal 0 by subtracting 3 on each side, resulting in x² + 6x - 16 = 0.

Front

How do you find the roots of a factored quadratic equation?

Back

Set each factor equal to zero and solve for x. For example, if (x + p)(x + q) = 0, then x + p = 0 or x + q = 0.

Front

What are the two numbers that add to 6 and multiply to -16?

Back

The two numbers are 8 and -2, since 8 + (-2) = 6 and 8 * (-2) = -16.

Front

What is the zero product property?

Back

The zero product property states that if the product of two factors is zero, then at least one of the factors must be zero.

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 vertex of a parabola?

Back

The vertex of a parabola is the highest or lowest point on the graph of a quadratic function, depending on its orientation.

Front

How can you check if your factored form is correct?

Back

You can check by expanding the factored form back into standard form and ensuring it matches the original equation.

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, there are two real roots; if zero, one real root; if negative, no real roots.