For this case, we have that the equation of the position is given by:

To find the velocity, we must derive the equation from the position.
We have then:

Then, we evaluate the derivative for time t = 8.
We have then:
Answer:
the instantaneous velocity at t = 8 is:
Answer:
just substitute the value of x as 1
f(x)=3(12)x+1
f(1)=3(12)(1)+1
f(1)=3(12)(1)+1
f(1)=36+1
f(1)=37
So since the vertex falls onto the axis of symmetry, we can just solve for that to get the x-coordinate of both equations. The equation for the axis of symmetry is
, with b = x coefficient and a = x^2 coefficient. Our equations can be solved as such:
y = 2x^2 − 4x + 12: 
y = 4x^2 + 8x + 3: 
In short, the vertex x-coordinate's of y = 2x^2 − 4x + 12 is 1 while the vertex's x-coordinate of y = 4x^2 + 8x + 3 is -1.
Proportional and linear functions are almost identical in form. The only difference is the addition of the “b” constant to the linear function. Indeed, a proportional relationship is just a linear relationship where b = 0, or to put it another way, where the line passes through the origin (0,0).
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