Completing the Square

Completing the Square Equation

a (x + h)² + q

What does a, h and q represent?

The sign of the a value tells if the function has a minimum or maximum value
- If a is a negative number the function will have a maximum value
- If a is a positive number the function will have a minimum value

The q value is either the maximum or minimum value depending on what sign a has

The opposite of the h value is our axis of symmetry so that -(b/2a)

Formula for h

b/2a

Formula for q

c - (b²/4a)

Coordinates of Turning Point

(x,y)
where x = axis of symmetry
y = q value

Roots of f(x) = 0

Solve for x (remember square root is +-)

Value of y where quadratic cuts

When x = 0
(Quadratic Equation)

Completing the Square