Quadratic Formula

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 ax² + bx + c = 0.

Front

What does it mean for a quadratic equation to be factored?

Back

Factoring a quadratic equation means expressing it as a product of two binomials, such as (px + q)(rx + s) = 0.

Front

What are the coefficients in the quadratic equation 4x² - 8x - 3 = 0?

Back

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

Front

How do you convert a quadratic equation to standard form?

Back

To convert to standard form, rearrange the equation to the form ax² + bx + c = 0.

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. It 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.

Front

Solve the quadratic equation: x² - 5x + 6 = 0

Back

x = 2, x = 3.

Front

What is the vertex of a parabola represented by the quadratic equation y = ax² + bx + c?

Back

The vertex can be found using the formula (-b/(2a), f(-b/(2a))).