Completing the square

Front

What is completing the square?

Back

Completing the square is a method used to solve quadratic equations by rewriting them in the form (x + p)² = q, making it easier to find the roots.

Tags

CCSS.HSA-REI.B.4B

Front

What is the first step in completing the square for the equation x² + 6x = 5?

Back

Subtract 5 from both sides to get x² + 6x - 5 = 0.

Tags

CCSS.HSA-REI.B.4B

Front

How do you find the value to complete the square for x² + 10x?

Back

Take half of the coefficient of x (which is 10), square it (5² = 25), and add it to both sides.

Tags

CCSS.HSA-REI.B.4B

Front

What is the formula for completing the square?

Back

The formula is (x + b/2)² - (b/2)² = c, where b is the coefficient of x.

Tags

CCSS.HSA-REI.B.4B

Front

What does it mean to 'move' a term in an equation?

Back

To 'move' a term means to isolate it on one side of the equation, typically by adding or subtracting it from both sides.

Tags

CCSS.6.EE.B.7

Front

What is the completed square form of x² + 12x = 5?

Back

(x + 6)² = 41.

Tags

CCSS.HSA-REI.B.4B

Front

How do you solve for x after completing the square?

Back

Take the square root of both sides, then solve for x by isolating it.

Tags

CCSS.HSA-REI.B.4B

Front

What is the significance of the vertex in a quadratic equation?

Back

The vertex represents the maximum or minimum point of the parabola represented by the quadratic equation.

Front

What is the relationship between the coefficients and the vertex of a quadratic equation in standard form?

Back

For a quadratic equation ax² + bx + c, the x-coordinate of the vertex is given by -b/(2a).

Front

What is the first step to solving a quadratic equation by completing the square?

Back

Rearrange the equation to isolate the constant term on one side.

Tags

CCSS.HSA-REI.B.4B