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.

Tags

CCSS.HSA-REI.B.4B

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.

Tags

CCSS.HSA-REI.B.4B

Front

What does it mean if the discriminant is positive?

Back

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

Tags

CCSS.HSA-REI.B.4B

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).

Tags

CCSS.HSA-REI.B.4B

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).

Tags

CCSS.HSA-REI.B.4B

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.

Tags

CCSS.HSA-REI.B.4B

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.

Tags

CCSS.HSA-REI.B.4B

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.

Tags

CCSS.HSA-REI.B.4B

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.

Tags

CCSS.HSA-REI.B.4B