Flashcard Review: Solve by Factoring and Extracting Roots

Front

What is the process of solving a quadratic equation by factoring?

Back

To solve a quadratic equation by factoring, express the equation in the form of (ax + b)(cx + d) = 0, then set each factor equal to zero and solve for x.

Front

Back

x = -2 and x = -\frac{3}{5}

Front

What are the roots of the equation (x − 5)(x + 4) = 0?

Back

x = 5 and x = -4

Front

Solve for x: (8x + 5)(x + 1) = 0

Back

x = -\frac{5}{8} and x = -1

Front

What does it mean for a quadratic equation to have real roots?

Back

A quadratic equation has real roots if its discriminant (b^2 - 4ac) is greater than or equal to zero.

Front

Back

n = -9 and n = 3

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

Back

x = 0 and x = 7

Front

What is a quadratic equation?

Back

A quadratic equation is a polynomial equation of the form ax^2 + bx + c = 0, where a, b, and c are constants and a ≠ 0.

Front

How do you find the vertex of a quadratic function?

Back

The vertex of a quadratic function in the form y = ax^2 + bx + c can be found using the formula x = -\frac{b}{2a}.