9 Consider the following equation y 7 8x x2 a Find the ver

9. Consider the following equation.

y = 7 + 8x x²

(a) Find the vertex of the graph of the equation.
(x, y) = (______)

(b) Determine if the vertex is a maximum or minimum point.

maximum

minimum

(c) Determine what value of x gives the optimal value of the function.
x = ______

(d) Determine the optimal (maximum or minimum) value of the function.
y = ______

Solution

given y = 7 + 8x x²

y = x² +8x +7

y =-(x²-8x)+7

y =-(x²-8x+16-16)+7

y =-(x²-8x+16)+16+7

y =-(x-4)²+23

a)vertex (x,y)=(4,23)

b)vertex is a maximum point since graph is open downwards

c)x=4 gives optimum value of function

d)y=23 is maximum value of function