5.5&5.6 HW Completing the Square and Solving Complex

Front

What is a perfect square trinomial?

Back

A perfect square trinomial is a quadratic expression that can be expressed as the square of a binomial. It takes the form: (a + b)² = a² + 2ab + b².

Front

How do you find the value of c to make x² - 14x + c a perfect square trinomial?

Back

To find c, take half of the coefficient of x (which is -14), square it: (-14/2)² = 49. Thus, c = 49.

Front

What is the process of completing the square?

Back

Completing the square involves rearranging a quadratic equation into the form (x - p)² = q, where p and q are constants. This allows for easier solving of the equation.

Front

Solve the equation by completing the square: x² + 12x = 5.

Back

Rearranging gives x² + 12x - 5 = 0. Completing the square results in (x + 6)² = 41, leading to x = 6 ± √41.

Front

Back

The simplified form is 10√2.

Front

When factoring x² - 4x + 4 = 20, what goes in the blank? (x - __ )² = 20

Back

The blank is filled with 2, so (x - 2)² = 20.

Front

How do you solve the equation x² + 6x - 4 = 36 by completing the square?

Back

Rearranging gives x² + 6x - 40 = 0. Completing the square results in (x + 3)² = 49, leading to x = -3 ± 7.

Front

What is the formula for completing the square for a quadratic equation ax² + bx + c?

Back

The formula is: x = -b/(2a) ± √(b² - 4ac)/(2a). This gives the vertex and roots of the quadratic.

Front

What does it mean to simplify a square root?

Back

Simplifying a square root means expressing it in its simplest form, removing any perfect square factors.

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.