SOLUTION: For the following: f(x)= 5x^2-70x+227, I need to find: Shifted Form Range x-Intercept y-intercept I already found the domain and vertex, but I am having a problem finding th

Algebra ->  Quadratic-relations-and-conic-sections -> SOLUTION: For the following: f(x)= 5x^2-70x+227, I need to find: Shifted Form Range x-Intercept y-intercept I already found the domain and vertex, but I am having a problem finding th      Log On


   

Question 1128907: For the following: f(x)= 5x^2-70x+227, I need to find:
Shifted Form
Range
x-Intercept
y-intercept
I already found the domain and vertex, but I am having a problem finding the range, and the x and y-intercepts.
Answer by MathLover1(20850) About Me  (Show Source):
You can put this solution on YOUR website!
f%28x%29=+5x%5E2-70x%2B227.....complete square
f%28x%29=+%285x%5E2-70x%29%2B227
f%28x%29=+5%28x%5E2-14x%29%2B227
f%28x%29=+5%28x%5E2-14x%2Bb%5E2%29-5b%5E2%2B227=> coefficient 2ab=14, a=1=>b=7%29%29%29%0D%0A%0D%0A%7B%7B%7Bf%28x%29=+5%28x%5E2-14x%2B7%5E2%29-5%2A7%5E2%2B227
f%28x%29=+5%28x-7%29%5E2-245%2B227
f%28x%29=5+%28x+-+7%29%5E2+-+18

=> h=7, k=-18
vertex is global minimum at (7, -18)

Shifted: original function f%28x%29=x%5E2 is shifted 7 units to the right
Range:
{ y element R : y%3E=-18 }


x-Intercept:
0=5+%28x+-+7%29%5E2+-+18
18=5%28x+-+7%29%5E2
18%2F5+=%28x+-+7%29%5E2
sqrt%2818%2F5%29+=x+-+7
x=7%2Bsqrt%2818%2F5%29+ or x=7-sqrt%2818%2F5%29

approximately x=8.9 or x=5.1
x- intercepts are at (10.6, 0) and (3.4, 0)


y-intercept:
f%28x%29=5+%280+-+7%29%5E2+-+18
f%28x%29=5+%28+-+7%29%5E2+-+18
f%28x%29=5+%2849%29+-+18
f%28x%29=227
y-intercept is at (0, 227)