Solving Quadratics Review

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 ax² + bx + c = 0.

Front

What does it mean to make an equation equal to 0?

Back

Making an equation equal to 0 is the first step in solving quadratic equations, allowing us to apply methods like factoring or the quadratic formula.

Front

How do you identify a, b, and c in a quadratic equation?

Back

In the standard form ax² + bx + c = 0, a is the coefficient of x², b is the coefficient of x, and c is the constant term.

Front

What is the first step in solving x² + 6x - 13 = 3?

Back

The first step is to make it equal to 0 by subtracting 3 from both sides, resulting in x² + 6x - 16 = 0.

Front

What are the roots of the equation (x + 2)(x - 3) = 0?

Back

The roots are x = -2 and x = 3.

Front

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

Back

If a quadratic equation cannot be factored, it means that its roots are not rational numbers, and the quadratic formula may be used to find the solutions.

Front

What is the discriminant in the quadratic formula?

Back

The discriminant is the part of the quadratic formula under the square root, b² - 4ac, which determines the nature of the roots.

Front

What does a positive discriminant indicate?

Back

A positive discriminant indicates that the quadratic equation has two distinct real roots.

Front

What does a zero discriminant indicate?

Back

A zero discriminant indicates that the quadratic equation has exactly one real root (a repeated root).

Front

What does a negative discriminant indicate?

Back

A negative discriminant indicates that the quadratic equation has no real roots, but two complex roots.