Solve Quadratic Equations by Factoring or the Quadratic Formula

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 are the values of a, b, and c in the equation 4x² - 8x = 3?

Back

a = 4, b = -8, c = -3.

Front

How do you solve a quadratic equation by factoring?

Back

To solve by factoring, rewrite the equation in the form (px + q)(rx + s) = 0, then set each factor to zero and solve for x.

Front

What is the quadratic formula?

Back

The quadratic formula is x = (-b ± √(b² - 4ac)) / (2a), used to find the roots of a quadratic equation.

Front

What does the discriminant (b² - 4ac) tell us?

Back

The discriminant indicates the nature of the roots: if > 0, two distinct real roots; if = 0, one real root; if < 0, no real roots.

Front

Solve the equation y² + 10y = -9 using the quadratic formula.

Back

The solutions are y = -1 and y = -9.

Front

What is the first step in solving a quadratic equation by the quadratic formula?

Back

Rearrange the equation to the standard form ax² + bx + c = 0.

Front

How can 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 it.

Front

What is the vertex form of a quadratic equation?

Back

The vertex form is y = a(x - h)² + k, where (h, k) is the vertex of the parabola.

Front

What is the axis of symmetry in a quadratic function?

Back

The axis of symmetry is the vertical line x = -b/(2a) that divides the parabola into two mirror images.