SOLUTION: Given the quadratic function f(x)= ax^2+bx+10 has a maximum point (2,18). (a) Without using the differentiation method or drawing a graph, determine the values of a and b. (b)Ske

Algebra ->  Graphs -> SOLUTION: Given the quadratic function f(x)= ax^2+bx+10 has a maximum point (2,18). (a) Without using the differentiation method or drawing a graph, determine the values of a and b. (b)Ske      Log On


   

Question 859424: Given the quadratic function f(x)= ax^2+bx+10 has a maximum point (2,18).
(a) Without using the differentiation method or drawing a graph, determine the values of a and b.
(b)Sketch the graph of the function f(x). Hence, find the range of f(x) for the domain 0 (< or =) x (< or =) 3
Answer by Fombitz(32388) About Me  (Show Source):
You can put this solution on YOUR website!
So you need to get to vertex form that looks like,
ax%5E2%2Bbx%2B10=-c%28x-2%29%5E2%2B18
ax%5E2%2Bbx%2B10=-cx%5E2%2B4cx-4c%2B18
Where
a=-c
b=4c%5D%7D%7D%0D%0A%7B%7B%7B-4c%2B18=10
-4c=-8
c=2
So then,
b=4%282%29=8
a=-2
-2x%5E2%2B8x%2B10=-2%28x-2%29%5E2%2B18