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Find a for the parabola: Y-5=a(x-4)^2 that passes through (5,3)

All that needs to be done is to put (5,3) is for (x,y) and solve for a.

That gives 3-5 = a(5-4)^2. Since 3-5 = -2 and 5-4 = 1, and squaring it leaves it as 1,

we have -2 = a.

This makes the parabola into Y - 5 = -2(X-4)^2.

Looking back at Y - 5 = a(x-4)^2, it can be seen that a = -2.

To do it even further than requested, put the answer in the form Y = aX² + bX + c.

That can be multiplied out to give Y - 5 = -2(X² - 8X + 16).

That is Y - 5 = 2X² + 16X - 32.

Adding 5 to both sides gives Y = 2X² + 16X - 27.

Algebra

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