Describe the key features of the graph of the quadratic function f(x) = x2 - 8x - 20

a. does the parabola open up or down?
b. is the vertex a minimum or a maximum?
c. identify the axis of symmetry, vertex and the y-intercept of the parabola.

If f(x)=x^2-8x-20 then

dy/dx=2x-8 and d2y/dx2=2

A) Since acceleration is a constant positive the parabola opens upward.

B) Since acceleration is a constant positive the parabola will have a vertex at an absolute minimum

C)  The vertex will occur when dy/dx=0, 2x-8=0, 2x=8, x=4

So the axis of symmetry is the vertical line x=4.

The vertex is y(4)=-36, corresponding to the vertex point (4,-36)

The y-intercept occurs when x=0, y(0)=-20, so the y-intercept is the point (0,-20)

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