Question 181398
For the quadratic function f(x) = x^2 + 2x -8 Find: 
a. THe axis of symmetry and the vertex. 
b. THe x-intercepts and y intercepts. 
c. The domain and range. 
d. Does the function have a maximum or minimum value. 
:
first lets complete the square
:
{{{y=(x^2+2x+1)-1-8}}}
:
{{{y=(x+1)^2-9}}}
:
vertex is at (-1,-9)
axis of symmetry is x=-1
:
y intercept is found by setting x to zero--->y=0+0-8
so y intercept is -8: (0,-8)
:
x intercept is found by setting y to zero--->{{{x^2+2x-8=0}}}
{{{(x-2)(x+4)=0}}}
:
x intercepts are 2 and -4: (2,0) and (-4,0)
:
domain is all real numbers: range is all real {{{y>=-9 }}}
:
function has a minimum value:
:
{{{graph(300,300,-10,10,-10,10,x^2+2x-8)}}}