Part A Consider the function represented by y=x^2+8x+10.

Question

Complete the square to create an equivalent function. Which equation represents an equivalent function after completing the square?

y=(x+^4)2−6

y=(x+4)^2+10

y=(x+8)^2-6

y=(x+8)^2+10

Part B Consider the function represented by .

Select and drag a word and numbers to the empty boxes to correctly complete the sentence about the minimum or maximum value of the function

The function has a value at ( )

minimum, maximum, -4, -3, -1, 0, 1, 3, 4,

Answer 1

Completing the square:

y = x² + 8x + 10 = x² + 2•4•x +16 + 10 - 16 = (x + 4)² - 6

y = (x -(-4))² + (-6) ← equation of parabola in the vertex form

Coordinates of the vertex: (-4, -6)

Coefficient of "x²" is "1" - positive number - so, the parabola opens upward and the vertex is the lowest point of the parabola, i.e. y-coordinate of the vertex is the smallest value of the function "y".

Function has a "-6" value at (- 4)