Complete the square

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 adding and subtracting the square of half the coefficient of x.

Front

How do you find the value to complete the square for the expression x² - 14x?

Back

To complete the square, take half of -14 (which is -7), square it (resulting in 49), and add it to the expression: x² - 14x + 49.

Front

What is a perfect square trinomial?

Back

A perfect square trinomial is a quadratic expression that can be factored into the square of a binomial, such as (x + a)² or (x - a)².

Front

What value of c makes x² + 34x + c a perfect square trinomial?

Back

To find c, take half of 34 (which is 17), square it (resulting in 289), so c = 289.

Front

How do you determine the missing value in the expression x² + 12x + ____?

Back

To find the missing value, take half of 12 (which is 6), square it (resulting in 36), so the expression becomes x² + 12x + 36.

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), where the term b² - 4ac is the discriminant.

Front

What is the significance of the discriminant in completing the square?

Back

The discriminant (b² - 4ac) determines the nature of the roots of the quadratic equation. If it's positive, there are two real roots; if zero, one real root; if negative, no real roots.

Front

How do you complete the square for the expression x² + 26x + ___?

Back

Take half of 26 (which is 13), square it (resulting in 169), so the missing value is 169.

Front

What is the relationship between completing the square and the vertex form of a quadratic function?

Back

Completing the square transforms a quadratic function into vertex form, y = a(x - h)² + k, where (h, k) is the vertex of the parabola.

Front

How can completing the square be used to solve quadratic equations?

Back

By rewriting the equation in the form (x - p)² = q, you can then take the square root of both sides to find the values of x.