How do you find the minimum value of a quadratic function?

In this lesson you will learn to rewrite a quadratic function to reveal the minimum value by completing the square.

Let’s Review Suppose we have

Complete or exact square (x+a) 2 (x+a)(x+a) X 2 +2ax+a 2

A Common Mistake Forgetting to preserve equality =(x 2 -10x ) +32 =(x-5) y=(x-5) Add and subtract the same number to keep the equality

Let’s Review Core Lesson y=x 2 -12x+49 =(x 2 -12x )+49 =(x-6) 2 square- always positive unless it’s zero

Let’s Review Core Lesson ADDING a positive number to any number makes that number bigger so the function will have a minimum value when the square term is zero.

Let’s Review Core Lesson y =(6-6) smallest number

Let’s Review Core Lesson x(x-6) 2 +13y (1-6) (6-6) (7-6) (0-6) The minimum value is 13 when x=6 y=(x-6)

In this lesson you have learned to rewrite a quadratic function to reveal the minimum value by completing the square

Let’s Review Guided Practice Rewrite y=x 2 +8x+3 by completing the square. What is the minimum value of this quadratic function?

Let’s Review Extension Activities Partner matching cards. Write each polynomial and ordered pair on index cards. Shuffle all 12 cards then match each function with its equivalent form and corresponding minimum value. y=x 2 +16x+64 y=(x+8) 2 (-8,0) y=x 2 -2x-9 y=(x-1) (1,-10) y=x 2 +26x+68 y=(x+13) (-13,-101 y=x 2 +18x-4 y=(x+9) (-9/-85)

Let’s Review Extension Activities Write a quadratic function whose graph has the given characteristics 1. Minimum: (6,1) point on the graph: (4,5) 2. Points on the graph: (1,7), (4,-2), (5,-1) 3. X-intercepts (5,0) (-4,0)

Let’s Review Quick Quiz Rewrite each function to find its minimum value by completing the square.  y=x 2 -3x+9  y=x 2 +12x+24