Question

Convert this quadratic function to vertex form.

y=x^2+14x+48
Then determine the minimum value of the function.


Points: Concept Addressed:

3 = Correctly completes the square to convert the function into vertex form.

2 = Correctly determines the minimum value of the function.

Answer 1

`y=x^2+14x+48=\underbrace{x^2+2x\cdot7+7^2}_(use:(a+b)^2=a^2+2ab+b^2)-7^2+48=(x+7)^2-49+48=(x+7)^2-1`

The coordinates of the vertex: (-7; -1).
The minimum value of the vertex is equal -1.