5.6-5.7 Quadratic Formula/Complete Square (Lee 24-25)

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 completing the square mean?

Back

Completing the square is a method used to solve quadratic equations by rewriting the equation in the form (x - p)² = q, making it easier to solve for x.

Front

Solve by completing the square: x² − 12x + 23 = 0

Back

x = 6 ± √13.

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: 4x² – 8x – 3 = 0

Back

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

Front

What is the discriminant in the Quadratic Formula?

Back

The discriminant is the part of the formula under the square root: b² - 4ac. It determines the nature of the roots.

Front

What does a positive discriminant indicate?

Back

A positive discriminant indicates that there are two distinct real solutions to the quadratic equation.

Front

What does a zero discriminant indicate?

Back

A zero discriminant indicates that there is exactly one real solution (a repeated root) to the quadratic equation.

Front

What does a negative discriminant indicate?

Back

A negative discriminant indicates that there are no real solutions, only complex solutions.

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.