SOLUTION: graph the function g(x)=-0.5x^2 then describe g(x) when compared to f(x)=x^2

Algebra ->  Coordinate-system -> SOLUTION: graph the function g(x)=-0.5x^2 then describe g(x) when compared to f(x)=x^2      Log On


   

Question 1210580: graph the function g(x)=-0.5x^2 then describe g(x) when compared to f(x)=x^2
Answer by MathLover1(20855) About Me  (Show Source):
You can put this solution on YOUR website!

g%28x%29++=+f%28x%29+%2B+C
if C+%3E+0 moves it up
if C+%3C+0 moves it down
in your case C=0, so g%28x%29 passes through origin and does not move

y+=+Cf%28x%29
if C+%3E+1 stretches it in the y-direction
if 0+%3C+C+%3C+1 compresses it
in your case C=-0.5 or -1%2F2, so g%28x%29 compresses 2 times in y-direction
since C=-0.5, g%28x%29 will be flipped upside down :

g%28x%29+=+-0.5x%5E2

since g%28x%29+=+-f%28x%29 reflects it about x-axis

so, g%28x%29+compressed 2 times in y-direction , flipped upside down, and reflected about x-axis

+graph%28+600%2C+600%2C+-10%2C+10%2C+-10%2C+10%2C+-0.5x%5E2%2C+x%5E2%29+