Find a parabola with equation Find a parabola with equation y = ax2 + bx + c tha

Question

Find a parabola with equation

Find a parabola with equation y = ax2 + bx + c that has slope 12 at x = 1, slope -16 at x = -1, and passes through the point (1, 9). y = Find the derivative of the function using the definition of derivative. State the domain of the function and the domain of its derivative. g(t) = 7t/t + 10a On the same coordinate axes, sketch graphs (as accurately as possible) of the functions y = x3 - 2X2 - x + 4 and y =-x2 + llx + 4. On the basis of your sketch in part (a), at how many points do the two graphs appear to intersect? Find the coordinates of all intersection points, (x, y) =(' 1) (smallest x-value) (x, y) =(' ) (x, y) =(' 1) (largest x-value)

Explanation / Answer

y=ax^2+bx+c

y'= 2ax+b
given slope =12 at x=1
and slope = -16 at x=-1

so
12=2a+b
-16=-2a + b

adding
-4=2b
b=-2 and a=7

y=7x^2 - 2x + c

this passes through (1,9)

9=7-2+c
c=4

y=7x^2 - 2x + 4

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