Question

Rewrite the following quadratic function in vertex form. Then, determine if it has a maximum or minimum and say what that value is. y = -x^2 + 6x + 5

Answer 1

Discussion

1. Put brackets around the first two terms

y = (-x^2 + 6x) + 5

2. Take out the common factor of -1

y = -(x^2 - 6x) + 5

3. Inside the brackets, take 1/2 of - 6 and square it

y = -(x^2 - 6x + ( - 6 / 2)^2 )  + 5

y = -(x^2 - 6x +  (- 3)^2 )  )  + 5

y = -(x^2 - 6x + 9 ) + 5

Note: Step 3 is very long. Make sure you work your way through it

4. You have added 9 inside the brackets. It is actually - 9. So add 9 outside to balance the equation out. This is the key step. Make sure you understand it.

y = - (x^2 - 6x + 9) + 5 + 9

5. Express the brackets as a square.

y = - (x + 3)^2 + 14

Discussion

The equation is now in vertex form. The minus tells you that the equation is a maximum. The maximum is located at ( - 3, 14 )

A graph follows to show the results.