SOLUTION: For each quadratic function, (a) find the vertex, the axis of symmetry, and the maximum or minimum function value and (b) graph the function. {{{f(x)=1/2}}}{{{x^2+4x+19/3}}}

Algebra ->  Quadratic Equations and Parabolas -> SOLUTION: For each quadratic function, (a) find the vertex, the axis of symmetry, and the maximum or minimum function value and (b) graph the function. {{{f(x)=1/2}}}{{{x^2+4x+19/3}}}      Log On


   

Question 748054: For each quadratic function, (a) find the vertex, the axis of symmetry, and the maximum or minimum function value and (b) graph the function.
f%28x%29=1%2F2x%5E2%2B4x%2B19%2F3
Answer by josgarithmetic(39617) About Me  (Show Source):
You can put this solution on YOUR website!
This solution will be taken part of the way only:

f%28x%29=%281%2F2%29x%5E2%2B4x%2B19%2F3, complete the square,..
f%28x%29=%281%2F2%29%2A%28x%5E2%2B8x%2B38%2F3%29
The term necessary will be %288%2F2%29%5E2=16
f%28x%29=%281%2F2%29%28x%5E2%2B8x%2B16%2B38%2F3-16%29
f%28x%29=%281%2F2%29%28%28x%2B4%29%5E2%2B%2838-3%2A16%29%2F3%29
f%28x%29=%281%2F2%29%28%28x%2B4%29%5E2%2B2%2A%2819-3%2A8%29%2F3%29
f%28x%29=%281%2F2%29%28%28x%2B4%29%5E2%2B2%2A6%2F3%29
f%28x%29=%281%2F2%29%28%28x%2B4%29%5E2%2B2%2A2%29
highlight%28f%28x%29=%281%2F2%29%28x%2B4%29%5E2%2B2%29

Now from the standard form of this function, the vertex, symmetry axis, and knowing that the vertex is either min or max can be read directly from the equation.

graph%28300%2C300%2C-10%2C12%2C-10%2C12%2C%281%2F2%29%28x%2B4%29%5E2%2B2%29