Quadratic Formula

Front

What is the quadratic formula?

Back

The quadratic formula is used to find the solutions (roots) of a quadratic equation and is given by: x = (-b ± √(b² - 4ac)) / (2a).

Front

Identify the values of a, b, and c in the equation: 4x² - 8x - 3 = 0.

Back

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

Front

What are the solutions of a quadratic equation called?

Back

The solutions of a quadratic equation are called roots, x-intercepts, or zeros.

Front

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

Back

Rearranging gives: 4x² - 8x - 3 = 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

If the discriminant is positive, what can be said about the roots?

Back

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

Front

If the discriminant is zero, what can be said about the roots?

Back

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

Front

If the discriminant is negative, what can be said about the roots?

Back

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

Front

Solve the quadratic equation: 2x² + 2x - 12 = 0 using the quadratic formula.

Back

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

Front

What is the vertex form of a quadratic equation?

Back

The vertex form is y = a(x - h)² + k, where (h, k) is the vertex of the parabola.