Review for Complete the Square and Quadratic Formula

Front

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

Back

The 'b' value is -8.

Front

Complete the square for the expression: x² + 6x + ____

Back

x² + 6x + 9.

Front

Write the quadratic expression x² + 8x - 1 in completed square form.

Back

(x + 4)² - 17.

Front

Use the quadratic formula to solve the equation: 2x² + 2x - 12 = 0

Back

The solutions are x = 2 and x = -3.

Front

In the quadratic formula, if b² - 4ac > 0, what does it indicate about the solutions?

Back

It indicates that the quadratic equation has two different real solutions.

Front

What is the quadratic formula?

Back

The quadratic formula is x = (-b ± √(b² - 4ac)) / (2a).

Front

What does completing the square involve?

Back

Completing the square involves rewriting a quadratic expression in the form (x - p)² + q.

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.

Front

How do you find the vertex of a quadratic function in standard form?

Back

The vertex can be found using the formula h = -b/(2a) and then substituting h back into the equation to find k.

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 real solutions; = 0, one real solution; < 0, no real solutions.