SOLUTION: find vertex with vertex formula. find where f is increasing and decreasing f(x)= -4/5^2 - 1/5x +1

Algebra ->  Quadratic Equations and Parabolas -> SOLUTION: find vertex with vertex formula. find where f is increasing and decreasing f(x)= -4/5^2 - 1/5x +1      Log On


   

Question 408258: find vertex with vertex formula. find where f is increasing and decreasing
f(x)= -4/5^2 - 1/5x +1
Answer by MathLover1(20849) About Me  (Show Source):
You can put this solution on YOUR website!
f%28x%29=-%284%2F5%29x%5E2+-+%281%2F5%29x%2B1

The vertex is found using the formula for (x,y):
(-b/2a,f(-b/2a))
find x
x=-b%2F2a
=-%28-1%2F5%29%2F2%28-4%2F5%29
=0.2%2F%28-1.6%29
=-0.125...so we have (-0.125,y)..now find y
y=f%28-0.125%29
f%28-0.125%29=+-+%284%2F5%29%28-0.125%29%5E2+-+%281%2F5%29%28-0.125%29%2B1
f%281%29-0.125=-+%284%2F5%290.015625%2B0.025%2B1
f%28-0.125%29=1.0125................ so the vertex is (-0.125,1.0125)


the intervals on which the function is increasing and the intervals on which the function is decreasing
Given the vertex of (-0.125,1.0125):
The function is increasing on:
(-∞,-0.125)
The function is decreasing on:
(-0.125,∞)


+graph%28+500%2C+500%2C+-10%2C+10%2C+-10%2C+10%2C+-%284%2F5%29x%5E2+-+%281%2F5%29x+%2B1%29+