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

What does 'a' represent in a quadratic equation?

Back

In the quadratic equation ax² + bx + c = 0, 'a' is the leading coefficient, which determines the direction of the parabola (upward if a > 0, downward if a < 0).

Front

What does 'b' represent in a quadratic equation?

Back

In the quadratic equation ax² + bx + c = 0, 'b' is the coefficient of the linear term, which affects the position of the vertex of the parabola along the x-axis.

Front

What does 'c' represent in a quadratic equation?

Back

In the quadratic equation ax² + bx + c = 0, 'c' is the constant term, which represents the y-intercept of the parabola.

Front

How do you identify the vertex of a parabola from a quadratic equation?

Back

The vertex (h, k) of the parabola represented by the equation y = ax² + bx + c can be found using h = -b/(2a) and k = f(h).

Front

What is the discriminant in a quadratic equation?

Back

The discriminant is the part of the quadratic formula under the square root: b² - 4ac. It determines the nature of the roots: if > 0, two real roots; if = 0, one real root; if < 0, no real roots.

Front

Solve using the Quadratic Formula: x² + 4x - 40 = -8

Back

x = -8 or 4.

Front

Solve for x: 2x² - 8x - 24 = 0

Back

x = 6 or -2.

Front

Solve: 2x² + 7x - 15 = 0

Back

x = -5 or 1.5.

Front

Determine a, b, and c for the equation: 4x² - 8x = 3

Back

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