Quadratic Formula

Front

What is the Quadratic Formula?

Back

The Quadratic Formula is used to find the solutions of a quadratic equation in the form ax² + bx + c = 0. It is given by x = (-b ± √(b² - 4ac)) / (2a).

Front

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

Back

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

Front

Solve using the Quadratic Formula: x² + 4x + 3 = 0

Back

x = -1 and x = -3.

Front

What does the discriminant (b² - 4ac) tell us?

Back

The discriminant determines the nature of the roots of a quadratic equation: if > 0, two real solutions; if = 0, one real solution; if < 0, no real solutions.

Front

Use the quadratic formula to solve: 2x² + 2x - 12 = 0

Back

x = 2 and x = -3.

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.

Front

Solve using the Quadratic Formula: x² + 4x - 40 = -8

Back

x = -8 and x = 4.

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.

Front

How do you convert from standard form to vertex form?

Back

Complete the square on the quadratic equation in standard form.

Front

What is the axis of symmetry in a quadratic function?

Back

The axis of symmetry is the vertical line x = -b/(2a) that divides the parabola into two mirror images.