Without graphing, find the vertex, the axis of symmetry, and the maximum value or the minimum value.

f{x) = 5(x − 3)2 + 9

There are two ways to find the vertex without graphing, Can anyone explain both ways?

Question

Without graphing, find the vertex, the axis of symmetry, and the maximum value or the minimum value.

f{x) = 5(x − 3)2 + 9


There are two ways to find the vertex without graphing,  Can anyone explain both ways?

whpalmer4 · Answer

One way would be with calculus.  Take the first derivative of f(x), set it equal to 0, and solve for $x$.  That will give you the $x$ value of the vertex, and you can plug it back into the formula to find the corresponding value for $y$.  

Another way would be to look at the form of the equation.
$$y=5(x-3)^2+9$$is a parabola.  If you remember translating equations, this is a parabola which has been shifted 3 units along the $x$ axis, and 9 along the $y$ axis.  Where is the vertex of $y=x^2$?  Shift that 3 units in the same direction along the $x$ axis, and 9 units in the same direction along the $y$ axis, and you should have your vertex.

anonymous · Answer

vertex (3,9)  focus (3) 181/20 directrix y= 179/20 axis of symmetry is x=3