Solving Quadratics and 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

Solve using the quadratic formula: x² + 4x - 40 = -8

Back

x = -8 and x = 4

Front

Identify a, b, and c in the equation: 4x² - 8x = 3

Back

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

Front

What does the discriminant (b² - 4ac) tell us?

Back

The discriminant determines the nature of the roots of a quadratic equation: if it's positive, there are two real roots; if zero, one real root; if negative, no real roots.

Front

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

Back

x = -5/2 and x = 7

Front

What is the standard form of a quadratic equation?

Back

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

Front

Solve using the quadratic formula: n² = 9n - 20

Back

n = 4 and n = 5

Front

What is the vertex form of a quadratic equation?

Back

The vertex form of a quadratic equation is y = a(x - h)² + k, where (h, k) is the vertex of the parabola.

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-image halves, given by the formula x = -b/(2a).

Front

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

Back

x = 2 and x = 4