SOLUTION: let f(x)=-1/2x^2+2x+3 find and graph: a) the x-coordinate of vertex b) the y-coordinate of vertex c) the axis of symmetry d) the max/min value of f and which value it is e)

Algebra ->  Graphs -> SOLUTION: let f(x)=-1/2x^2+2x+3 find and graph: a) the x-coordinate of vertex b) the y-coordinate of vertex c) the axis of symmetry d) the max/min value of f and which value it is e)      Log On


   

Question 345419: let f(x)=-1/2x^2+2x+3
find and graph:
a) the x-coordinate of vertex
b) the y-coordinate of vertex
c) the axis of symmetry
d) the max/min value of f and which value it is
e) the x value that gives max/min value of f
Answer by Fombitz(32388) About Me  (Show Source):
You can put this solution on YOUR website!
f%28x%29=-%281%2F2%29x%5E2%2B2x%2B3
Complete the square to put the function into vertex form, y=a%28x-h%29%5E2%2Bk where (h,k) is the vertex.
f%28x%29=-%281%2F2%29%28x%5E2-4x%29%2B3
f%28x%29=-%281%2F2%29%28x%5E2-4x%2B4%29%2B3%2B4%2F2
f%28x%29=-%281%2F2%29%28x-2%29%5E2%2B5
a) h=2
b) k=5
c) The vertex lies on the axis of symmetry, x=2
d) k=5 since the coefficient of x%5E2 is negative the parabola opens downward and the value at the vertex is a maximum.
ymax=5
e) h=2
.
.
.