9-3 The Quadratic Formula

Front

What is the quadratic formula?

Back

The quadratic formula is x = (-b ± √(b² - 4ac)) / (2a), used to find the solutions of a quadratic equation ax² + bx + c = 0.

Front

Identify the values of a, b, and c in the equation 2x² - 4x + 1 = 0.

Back

a = 2, b = -4, c = 1.

Front

Solve using the quadratic formula: 3x² - 12x + 9 = 0.

Back

x = 3.

Front

What does the discriminant (b² - 4ac) tell us about a quadratic equation?

Back

The discriminant determines the nature of the roots: if > 0, two distinct real roots; if = 0, one real root; if < 0, no real roots.

Front

Solve using the quadratic formula: x² + 6x + 8 = 0.

Back

x = -2, 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

Solve using the quadratic formula: 4x² + 4x + 1 = 0.

Back

x = -0.5.

Front

Identify the values of a, b, and c in the equation 5x² + 3x - 2 = 0.

Back

a = 5, b = 3, c = -2.

Front

Solve using the quadratic formula: x² - 5x + 6 = 0.

Back

x = 2, x = 3.

Front

What is the standard form of a quadratic equation?

Back

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