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 the 'a' value in the equation y = 16x² - 8x - 24.

Back

The 'a' value is 16.

Front

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

Back

The 'b' value is -8.

Front

Identify the 'c' value in the equation y = 16x² - 8x - 24.

Back

The 'c' value is -24.

Front

What does the discriminant (b² - 4ac) tell us about a quadratic equation?

Back

The discriminant determines the nature of the roots of the quadratic equation. If it is positive, there are two distinct real roots; if it is zero, there is one real root; if it is negative, there are no real roots.

Front

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

Back

x = -5/2, x = 7.

Front

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

Back

x = -8, x = 4.

Front

Solve using the quadratic formula: 2x² + 7x - 15 = 0

Back

x = -5, x = 3/2.

Front

What is a quadratic equation?

Back

A quadratic equation is a polynomial equation of degree 2, typically in the form ax² + bx + c = 0, where a, b, and c are constants and a ≠ 0.

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 the coordinates (h, k) where h = -b/(2a) and k is the value of the quadratic function at h.