8-6 Quad Formula and the Discriminant

Front

What is the quadratic formula?

Back

The quadratic formula is given by x = (-b ± √(b² - 4ac)) / (2a), where a, b, and c are coefficients of the quadratic equation ax² + bx + c = 0.

Front

What does the discriminant of a quadratic equation represent?

Back

The discriminant (D) is the expression b² - 4ac in the quadratic formula. It determines the nature of the roots of the quadratic equation.

Front

What does it mean if the discriminant is positive?

Back

If the discriminant is positive, the quadratic equation has two distinct real solutions.

Front

What does it mean if the discriminant is zero?

Back

If the discriminant is zero, the quadratic equation has exactly one real solution (a repeated root).

Front

What does it mean if the discriminant is negative?

Back

If the discriminant is negative, the quadratic equation has no real solutions; the solutions are complex (imaginary).

Front

How do you rearrange a quadratic equation to use the quadratic formula?

Back

To use the quadratic formula, rearrange the equation into the standard form ax² + bx + c = 0.

Front

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

Back

In the equation 4x² - 8x - 3 = 0, a = 4, b = -8, and c = -3.

Front

How do you apply the quadratic formula to solve 9x² = 4 + 7x?

Back

First, rearrange to standard form: 9x² - 7x - 4 = 0. Then apply the quadratic formula with a = 9, b = -7, c = -4.

Front

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

Back

The first step is to ensure the equation is in the standard form ax² + bx + c = 0.

Front

What is the significance of the term '±' in the quadratic formula?

Back

The '±' indicates that there are two possible solutions: one for addition and one for subtraction.