Question 672140: f(x)=2x^(2)-20x+52
Find the vertex,the maxium and minimum value of the quadratic
function, the range ,the intervals where the function increases and decreases.
Answer by aaronwiz(69)   (Show Source):
You can put this solution on YOUR website! Hi, my name is Aaron I am in 10th grade and im in honors trig/pre-calc. I dont feel like doing my hw, so I will do my best to help you.
First lets find the vertex: -b/2a=20/4=5
We know the x coordinate is 5
now plug 5 back in to the function and get 2(25)-100+52=2
so the vertex is (5,2)
Now to find the the maximum, the function is an even degree function, therfore the end behavior on both sides is up. and the leading coef. is positive. Thus without any math we know this function's maximum is infinity.
To find minimum it is simply the lowest y coordinate. Since we all know a vertex is a quadratics absolute maximum or minimum ( it is minimum in this case, because the graph opens up) it is easy to find the minimum. Thus the answer is 2.
to find range. Since f(x) has no range or domain restrictions, holes or asymptotes and it is not a rational function we already have the answer. It is simply the minimum and maximum. In interval notation it is [2,infinity).
To find the last part, we already know the graph opens up and its a quadratic. So the turning point of the function is the vertex. It is decreasing to the left of the vertex. And increasing on the right. So decreasing on (negative infinity,5). and increasing on (5,infinity).
Hope I helped. If you need a better explanation please feel free to contact me. A note of thanks is always appreciated. Good luck
|
|
|
