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 are the values of a, b, and c in the equation x² - 6x + 14?

Back

a = 1, b = -6, c = 14.

Front

How do you identify 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

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 and distinct roots; if = 0, one real root; if < 0, no real roots.

Front

Solve using the Quadratic Formula: x² + 4x + 3 = 0

Back

x = -1 and x = -3.

Front

Solve using the Quadratic Formula: 2x² - x - 3 = 0

Back

x = 3/2 and x = -1.

Front

What is the first step in using the Quadratic Formula?

Back

Identify the coefficients a, b, and c from the quadratic equation.

Front

What is the significance of the '±' symbol in the Quadratic Formula?

Back

The '±' symbol indicates that there are two possible solutions for x, one for addition and one for subtraction.

Front

Solve using the Quadratic Formula: 2x² + 2x - 12 = 0

Back

x = 2 and x = -3.

Front

What is a real solution in the context of quadratic equations?

Back

A real solution is a value of x that satisfies the equation and is a real number.