Solving Quadratics 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 expressing it as a product of two binomials, such as (x - p)(x - q) = 0, where p and q are the roots of the equation.

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 x.

Front

Solve by factoring: x² + 3x - 18 = 0

Back

x = 3 and x = -6

Front

Solve by factoring: x² + 7x + 12 = 0

Back

x = -3 and x = -4

Front

Solve by factoring: x² - 9x + 20 = 0

Back

x = 4 and x = 5

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

How do you check if your solutions to a quadratic equation are correct?

Back

Substitute the solutions back into the original equation to see if they satisfy the equation.

Front

What is the significance of the coefficients in a quadratic equation?

Back

The coefficients a, b, and c determine the shape and position of the parabola represented by the quadratic equation.

Front

What is the vertex of a parabola?

Back

The vertex is the highest or lowest point of the parabola, depending on its orientation (opening upwards or downwards).