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.

Tags

CCSS.HSA-REI.B.4B

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.

Tags

CCSS.HSA-REI.B.4B

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.

Tags

CCSS.HSA.APR.C.4

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.

Tags

CCSS.HSA-REI.B.4B

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.

Tags

CCSS.HSA-REI.B.4B

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.

Tags

CCSS.HSA-REI.B.4B

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.

Tags

CCSS.HSA-REI.B.4B

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.

Tags

CCSS.HSA-REI.B.4B

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.

Tags

CCSS.HSA-REI.B.4B