Completing the square practice

Front

What is the process of completing the square in a quadratic equation?

Back

Completing the square involves rewriting a quadratic equation in the form (x - p)² = q, where p and q are constants. This is done by manipulating the equation to isolate the x² and x terms.

Front

What is the standard form of a quadratic equation?

Back

The standard form of a quadratic equation is ax² + bx + c = 0, where a, b, and c are constants and a ≠ 0.

Front

How do you find the value to complete the square for the expression x² - 4x?

Back

To complete the square, take half of the coefficient of x (which is -4), square it (which gives 4), and add it to both sides of the equation.

Front

What is the significance of the term (b/2)² in completing the square?

Back

The term (b/2)² is added to both sides of the equation to create a perfect square trinomial, allowing the equation to be factored into the form (x - p)².

Front

What is the first step in completing the square for the equation x² + 6x - 4 = 36?

Back

The first step is to move the constant term to the other side of the equation, resulting in x² + 6x = 40.

Front

How do you solve for x after completing the square?

Back

After rewriting the equation in the form (x - p)² = q, take the square root of both sides, then solve for x by isolating it.

Front

What do you do if the quadratic equation is not equal to zero when completing the square?

Back

If the quadratic equation is not equal to zero, first rearrange it so that one side equals zero before completing the square.

Front

What is the relationship between the roots of a quadratic equation and completing the square?

Back

Completing the square allows you to find the roots of the quadratic equation by expressing it in a form that reveals the solutions directly.

Front

What is the formula for finding the vertex of a parabola represented by a quadratic equation?

Back

The vertex of a parabola given by the equation y = ax² + bx + c can be found using the formula (-b/2a, f(-b/2a)).

Front

What happens to the graph of a quadratic function when completing the square?

Back

Completing the square helps to identify the vertex form of the quadratic function, which reveals the vertex and the direction of the parabola.