Write the equation of the quadratic function f(x) that satisfies all three properties below: -
contains the point (-4,-195), has the same shape as y=-3x², the x-coordinate of the vertex is 4.

f(x) = -3(x - 4)^2 - 3.

Step-by-step explanation:

As the vertex is at x = 4 and it is the same shape as  y = -3x^2  the vertex of y = -3x^2 ( x = 0) moves 4 units to the right so the form of the f(x) is

f(x) = -3(x - 4)^2 + c    where c is some constant.

Now when x = - 4  f(x) = -195 so:

-195 = -3(-4-4)^2 + c

-195 = -3*64 + c

c = -195 + 192 = -3.

So the required equation is f(x) = -3(x - 4)^2 - 3.

answer rather than having to add and subtract the measurements of the semi-circle, notice that the semicircle to the left of ad is actually identical in area to the blank semicircle-shaped space to the left of bc. so if we transferred the red semicircle into the blank space, we would end up with a square of side length 24 cm. the area of a square is s^2 = 24^2 = 676 cm^2.

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