Quadratic Formula

Front

What is the standard form of a quadratic equation?

Back

The standard form of a quadratic equation is ax² + bx + c = 0, where a, b, and c are constants and a ≠ 0.

Front

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

Back

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

Front

How do you rearrange the equation 4x² - 8x = 3 into standard form?

Back

To rearrange, subtract 3 from both sides: 4x² - 8x - 3 = 0.

Front

What is the quadratic formula?

Back

The quadratic formula is x = (-b ± √(b² - 4ac)) / (2a).

Front

How do you apply the quadratic formula to the equation 2m² = -2m + 12?

Back

First, rearrange to standard form: 2m² + 2m - 12 = 0. Then apply the quadratic formula.

Front

What are the solutions to the equation 2m² + 2m - 12 = 0 using the quadratic formula?

Back

The solutions are m = 2 and m = -3.

Front

How do you solve the equation 9x² = 4 + 7x using the quadratic formula?

Back

Rearrange to standard form: 9x² - 7x - 4 = 0, then apply the quadratic formula.

Front

What is the discriminant in the quadratic formula and what does it indicate?

Back

The discriminant is b² - 4ac. It indicates the nature of the roots: if > 0, two real roots; if = 0, one real root; if < 0, no real roots.

Front

What are the solutions to the equation 5x² + 3x - 3 = 0 using the quadratic formula?

Back

The solutions are x = (-3 ± √69) / 10.

Front

How do you solve the equation 2x² + 2x - 12 using the quadratic formula?

Back

First, rearrange to standard form: 2x² + 2x - 12 = 0. Then apply the quadratic formula.