SOLUTION: find the domain and range of this function: f(x)=-3x^2+23x-14

Question 605212: find the domain and range of this function: f(x)=-3x^2+23x-14
Answer by lwsshak3(11628) (Show Source): You can put this solution on YOUR website!
find the domain and range of this function:
f(x)=-3x^2+23x-14
complete the square
f(x)=-3(x^2-23x/3+(23/6)^2)-14+3*(23/6)^2
f(x)=-3(x-23/6)^2+30.08
This is an equation of a parabola that opens downwards.
Its standard form: y=-A(x-h)^2+k, (h,k)=(x,y) coordinates of the vertex
For given equation:
vertex:(23/6,30.08)≈(3.83,30.08)
Domain: all real numbers (-∞,∞)
Range:(-∞,30.08]
..
see graph below:

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