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

Identify the values of a, b, and c in the quadratic equation: 2x² - 4x + 3 = 0.

Back

a = 2, b = -4, c = 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 - 5x + 6 = 0.

Back

x = 2, 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.

Front

Identify the 'b' value in the quadratic equation: y = 3x² + 6x + 2.

Back

b = 6.

Front

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

Back

x = -2.

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.

Front

Identify a, b, and c for the quadratic equation: x² + 2x - 8 = 0.

Back

a = 1, b = 2, c = -8.

Front

Solve using the quadratic formula: 5x² - 20 = 0.

Back

x = 2, x = -2.