Determine The Value of k so that y=5xsquared+100x+k has a maximum of 205
I am really lost on this one
nickdutta: "Determine The Value of k so that y=5xsquared+100x+k has a maximum of 205."
The parabolic equation y = 5x^2 + 100x + k is a parabola opening upward,
i think, 205 is the minimum. I will try solving it,
y = 5x^2 + 100x + k
completing the square,
(y - k)/5 = x^2 + 20x + 100 - 100,
(y - 5)/5 + 100 = (x + 10)^2
(1/5)(y -(k - 500)) = (x + 10)^2,
remember this standard equation of parabola?
(x - h)^2 = (4p)(y - k)
the vertex is (h, k) which is (-10, k - 500)
Now the vertex has a coordinate of (-10, k - 500), where y = k - 500
Now we have y = 205 as (STATED) maximum or minimum, then
205 = k - 500,
205 + 500 = k,
705 = k,
thus y = 5x^2 + 100x + 705.
i made a graph,
My solution looks awkward
please double click the graph for a better view, any comment?