Unit 6 Lesson 6: Using the 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 the discriminant (b² - 4ac) indicate?

Back

The discriminant determines the nature of the roots of a 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: x² + 4x + 3 = 0

Back

x = -1 and x = -3

Front

Identify A, B, and C in the equation: 5x² + x - 18 = -9x + 3x²

Back

A = 2, B = 10, C = -18

Front

Solve: 2x² + 7x - 15 = 0

Back

x = -5 or x = 1.5

Front

What is factoring in relation to quadratic equations?

Back

Factoring is the process of expressing a quadratic equation as a product of its linear factors, which can then be set to zero to find the roots.

Front

Solve by factoring: x² - 9x + 20 = 0

Back

x = 4 and x = 5

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.

Front

What is the vertex of a parabola?

Back

The vertex of a parabola is the highest or lowest point on the graph, depending on whether it opens upwards or downwards.

Front

How do you determine if a quadratic opens upwards or downwards?

Back

A quadratic opens upwards if the coefficient of x² (a) is positive and downwards if it is negative.