Solving Quadratic Equations by Factoring

Front

What is a quadratic equation?

Back

A quadratic equation is a polynomial equation of degree 2, typically in 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 involves rewriting it as a product of two binomial expressions, such as (x - p)(x - q) = 0, where p and q are the solutions of the equation.

Tags

CCSS.HSA-REI.B.4B

Front

What are the steps to solve a quadratic equation by factoring?

Back

1. Write the equation in standard form (ax² + bx + c = 0). 2. Factor the quadratic expression. 3. Set each factor equal to zero. 4. Solve for the variable.

Tags

CCSS.HSA-REI.B.4B

Front

What are the solutions of the equation x² + 2x - 3 = 0?

Back

The solutions are x = 1 and x = -3, found by factoring the equation as (x - 1)(x + 3) = 0.

Tags

CCSS.HSA-REI.B.4B

Front

How do you find the zeros of a quadratic function?

Back

To find the zeros of a quadratic function, set the function equal to zero and solve for the variable, often by factoring.

Tags

CCSS.HSA-SSE.B.3B

CCSS.HSF-IF.C.8A

Front

What is the significance of the zeros of a quadratic function?

Back

The zeros of a quadratic function represent the x-values where the graph intersects the x-axis, indicating the solutions to the equation.

Tags

CCSS.HSF-IF.C.7A

Front

What is the first step in solving (x + 2)(x - 3) = 0?

Back

The first step is to set each binomial factor equal to zero: x + 2 = 0 and x - 3 = 0.

Tags

CCSS.HSA-REI.B.4B

Front

What are the solutions to the equation 8x² + 10x - 3 = 0?

Back

The solutions are x = -3/2 and x = 1/4, found by factoring the equation.

Tags

CCSS.HSA-REI.B.4B

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 when factoring is difficult.

Tags

CCSS.HSA-REI.B.4B

Front

What does it mean if a quadratic equation cannot be factored?

Back

If a quadratic equation cannot be factored, it may have irrational or complex solutions, which can be found using the quadratic formula.

Tags

CCSS.HSA-REI.B.4B