9.4 Part B: Solve Quadratic Equations - by Factoring

Front

What are the x-intercepts of a quadratic equation?

Back

The x-intercepts are the points where the graph of the quadratic equation crosses the x-axis, which occur when y = 0.

Front

How do you factor a quadratic equation in the form ax^2 + bx + c?

Back

To factor a quadratic equation, find two numbers that multiply to ac (the product of a and c) and add to b (the coefficient of x).

Front

What is the factored form of the equation x^2 + 5x + 6?

Back

(x + 2)(x + 3) = 0.

Front

What are the solutions of the equation (x - 4)(x + 1) = 0?

Back

x = 4 and x = -1.

Front

What does it mean to solve a quadratic equation by factoring?

Back

It means to express the quadratic equation in a product of binomials and then set each factor equal to zero to find the solutions.

Front

What is the first step in solving the equation x^2 - 9 = 0 by factoring?

Back

Rewrite it as (x - 3)(x + 3) = 0.

Front

What are the solutions of the equation x^2 + 2x - 8 = 0?

Back

x = 2 and x = -4.

Front

How do you check if your factored form of a quadratic equation is correct?

Back

Expand the factored form and see if it equals the original quadratic equation.

Front

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

Back

The discriminant (b^2 - 4ac) determines the nature of the roots: if positive, two real roots; if zero, one real root; if negative, no real roots.

Front

What is the factored form of the equation x^2 - 5x + 6?

Back

(x - 2)(x - 3) = 0.