Find the axis of symmetry and the vertex of the graph of f(x)=−6x2+24x−20

The vertex will be when the velocity is equal to zero:

df/dx=-12x+24  (using the power rule for differentiation)

df/dx=0 only when:

-12x+24=0  add 12x to both sides

12x=24 divide both sides by 12

x=2, we find the y value to be:

y(2)=-6(2^2)+24*2-20

y(2)=-24+48-20=4

So the vertex is the point (2,4)

And the axis of symmetry is the line x=2

Now if you do not yet do calculus...

The vertex will occur midway between the two zeros.

6x^2-24x+20=0  (using the Quadratic Formula for simplicity)

x=(24±√96)/12

x≈(1.1835, 2.8165)

Now the vertex occurs at the average of the zeros...

x=(1.1835+2.8165)/2=2  (as we saw earlier)

y(2)=4

Vertex is at (2,4) and axis of symmetry is the vertical line x=2