SOLUTION: 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 f

Algebra ->  Quadratic Equations and Parabolas -> SOLUTION: 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 f      Log On


   

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.

Answer by Mathtut(3670) About Me  (Show Source):
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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=%28x%5E2%2B2x%2B1%29-1-8
:
y=%28x%2B1%29%5E2-9
:
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%5E2%2B2x-8=0
%28x-2%29%28x%2B4%29=0
:
x intercepts are 2 and -4: (2,0) and (-4,0)
:
domain is all real numbers: range is all real y%3E=-9+
:
function has a minimum value:
:
graph%28300%2C300%2C-10%2C10%2C-10%2C10%2Cx%5E2%2B2x-8%29