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

Back

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

Front

Identify a, b, and c in the quadratic equation: -8x² + x + 7 = 0.

Back

a = -8, b = 1, c = 7.

Front

What is the first step in solving the equation: x² + 6x - 13 = 3?

Back

Subtract 3 from both sides.

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 real solutions; if = 0, one real solution; if < 0, no real solutions.

Front

Solve using the quadratic formula: 2x² - 9x - 35 = 0.

Back

x = -5/2, x = 7.

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 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.

Front

What is the significance of the 'a' value in a quadratic equation?

Back

The 'a' value determines the direction of the parabola: if a > 0, it opens upwards; if a < 0, it opens downwards.