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 values of A, B, and C in the equation: 3m² - 14 = 11m

Back

A=3, B=-11, C=-14

Front

Solve using the Quadratic Formula: 6x² + 12x - 1 = 0

Back

x = 0.08, -2.08

Front

Solve using the Quadratic Formula: 6x² - 11x - 52 = 0

Back

x = 4, -2.17

Front

Solve using the Quadratic Formula: 4v² - 1v - 18 = 0

Back

v = 2.25, -2

Front

Identify the values of A, B, and C in the equation: 11r² + 6r = 6

Back

A=11, B=6, C=-6

Front

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

Back

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

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 ≠ 0.

Front

How do you derive the Quadratic Formula from the standard form of a quadratic equation?

Back

By completing the square on the equation ax² + bx + c = 0, you can derive the Quadratic Formula.

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.