SOLUTION: Graph a parabola: Give the vertex,axis,range and domain. I am lost as to how to set these problems up. It has been 20 years since I was in school. Here is the problem: f(x)=x^2+10x

Algebra ->  Quadratic-relations-and-conic-sections -> SOLUTION: Graph a parabola: Give the vertex,axis,range and domain. I am lost as to how to set these problems up. It has been 20 years since I was in school. Here is the problem: f(x)=x^2+10x      Log On


   

Question 647763: Graph a parabola: Give the vertex,axis,range and domain. I am lost as to how to set these problems up. It has been 20 years since I was in school. Here is the problem: f(x)=x^2+10x+23
Answer by lwsshak3(11628) About Me  (Show Source):
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Graph a parabola: Give the vertex,axis,range and domain. I am lost as to how to set these problems up. It has been 20 years since I was in school. Here is the problem:
f(x)=x^2+10x+23
This is an equation of a parabola that opens upwards. (sign of lead coefficient>0)
Its standard form: (y=(x-h)^2+k, (h,k)=(x,y) coordinates of the vertex.
Complete the square:
f(x)=(x^2+10x+25)+23-25
f(x)=(x+5)^2-2
vertex: (-5,-2)
axis of symmetry: x=-5
Range: (-2,∞)
Domain: (-∞,∞)
see graph below:
+graph%28+300%2C+300%2C+-10%2C+10%2C+-10%2C+10%2Cx%5E2%2B10x%2B23%29+