Find the vertex
-16x^2 + 20,504x

Question

Find the vertex
 -16x^2 + 20,504x

anonymous · Answer

hi friend

anonymous · Answer

can u hurry up

anonymous · Answer

its like rabies

anonymous · Answer

if by vertex you mean the stationary point of that curve:
$$y = -16x^2 + 20504x$$$$\frac{dy}{dx}= -32x +20504$$ set the second equation equal to zero to find the point where the gradient of tangent = 0
$$ -32x +20504 =0$$$$x = \frac{20504}{32} = 640.75$$
this is the x coordinate, substitute into the first equation to get the y coordinate.

anonymous · Answer

Correct method finding the derivative, but for a quadratic function, you can use the relationship x=-b/2a to find the axis of symmetry (the x coordinate of the vertex).

anonymous · Answer

yes, although i would argue knowing where that relationship comes from is more important than putting numbers in a formula

anonymous · Answer

You are correct, but for an algebra student, the calculus might not be very accessible.

anonymous · Answer

fair point

anonymous · Answer

is there a geometric derivation of -b/2a ? im interested

anonymous · Answer

Comes from the process of completing the square.  The first term is -b/2a plus or minus something.  That puts the axis of symmetry there, midway between the two roots.