Quadratic Formula

Front

What is the standard form of a quadratic equation?

Back

Front

What are the values of a, b, and c in the quadratic equation 7x^2 - 4x + 3 = 5x^2 + 8?

Back

a = 2, b = -4, c = -5 after rearranging to standard form.

Front

How do you solve a quadratic equation using the quadratic formula?

Back

Front

What is the discriminant in a quadratic equation?

Back

Front

What does a positive discriminant indicate about the roots of a quadratic equation?

Back

A positive discriminant indicates that there are two distinct real roots.

Front

What does a negative discriminant indicate about the roots of a quadratic equation?

Back

A negative discriminant indicates that there are no real roots, but two complex roots.

Front

What does a zero discriminant indicate about the roots of a quadratic equation?

Back

A zero discriminant indicates that there is exactly one real root (a repeated root).

Front

Solve the quadratic equation 4x^2 + 4x + 1 = 0 using the quadratic formula.

Back

x = -1/2.

Front

What is the nature of the solutions for the equation x^2 + 2x - 63 based on its discriminant?

Back

The discriminant is 256, which is positive, indicating 2 real and rational solutions.

Front

How do you determine the nature of the solutions using the discriminant?

Back