SOLUTION: Let f(x) = {{{ (x^2 - 9x + 1)/8 }}} The graph of f is a ____ The minimum value of the function f is f( ____ ) = ____ The maximum value of the function on th

Algebra ->  Functions -> SOLUTION: Let f(x) = {{{ (x^2 - 9x + 1)/8 }}} The graph of f is a ____ The minimum value of the function f is f( ____ ) = ____ The maximum value of the function on th      Log On


   

Question 906490: Let f(x) = ++++%28x%5E2++++-+++++9x+%2B+1%29%2F8++++

The graph of f is a ____
The minimum value of the function f is
f( ____ ) = ____
The maximum value of the function on the interval [-1 , 9 ] is
f( ____ ) = ____ .
* The graph of function g is created by
* stretching the graph of f vertically by a factor of 16,
* then shifting that graph up 27 units,
* and finally shifting the graph left 1 units.
Find the function g.
g(x)= ____
Answer by josgarithmetic(39617) About Me  (Show Source):
You can put this solution on YOUR website!
f%28x%29=%28x%5E2-9x%2B1%29%2F8, As meant when given,

f%28x%29=%281%2F8%29%28x%5E2-9x%2B1%29, a bit neater to handle;
The factor 1%2F8 squashes the parabola vertically.

The square term to use for transforming into standard form is %28-9%2F2%29%5E2=81%2F4.

f%28x%29=%281%2F8%29%28x%5E2-9x%2B1%2B81%2F4-81%2F4%29

f%28x%29=%281%2F8%29%28x%5E2-9x%2B81%2F4%2B1-81%2F4%29
f%28x%29=%281%2F8%29%28%28x%5E2-9x%2B81%2F4%29%2B1-81%2F4%29
f%28x%29=%281%2F8%29%28%28x-9%2F2%29%5E2%2B4%2F4-81%2F4%29
f%28x%29=%281%2F8%29%28x-9%2F2%29%5E2%2B%281%2F8%29%28-77%2F4%29
highlight%28f%28x%29=%281%2F8%29%28x-9%2F2%29%5E2-77%2F32%29----Standard Form.

The vertex, a minimum point of the function, is highlight%28x=9%2F2%29, highlight%28y=-77%2F32=-2%2613%2F32%29


Set f(x)=0 and solve for x to know the x-intercepts.
Set x=0 and solve for y to know the y-intercept.