Quadratic Formula

Front

What is the Quadratic Formula?

Back

The Quadratic Formula is used to find the solutions (or roots) 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 equation: 4x² - 8x = 3.

Back

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

Front

How many zeros can a quadratic equation have?

Back

A quadratic equation can have 0, 1, or 2 zeros.

Front

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

Back

x = -5/2, x = 7.

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 about a quadratic equation?

Back

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

Front

What is the vertex of a parabola represented by a quadratic equation?

Back

The vertex is the highest or lowest point of the parabola, found at x = -b/(2a).

Front

What is the axis of symmetry in a quadratic function?

Back

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

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.

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.