Quadratic formula

Front

What is the quadratic formula?

Back

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

Front

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

Back

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

Front

What does the 'a' value represent in a quadratic equation?

Back

The 'a' value represents the coefficient of x² and determines the direction of the parabola (upward if a > 0, downward if a < 0).

Front

Identify the 'b' value in the quadratic equation: y = 16x² - 8x - 24.

Back

b = -8.

Front

What is the significance of the discriminant (b² - 4ac) in the quadratic formula?

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 for x using the quadratic formula: 2x² - 4x - 6 = 0.

Back

x = 3, x = -1.

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 vertex of the quadratic function: y = 2(x - 3)² + 4.

Back

The vertex is (3, 4).

Front

What is the axis of symmetry in a quadratic function?

Back

The axis of symmetry is the vertical line that passes through the vertex, given by x = h in vertex form.

Front

Convert the standard form of a quadratic equation to vertex form: y = x² - 6x + 8.

Back

y = (x - 3)² - 1.