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Algebra/Algerbra 2: parabolas

Question
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

Volunteer

Scott A Wilson

Expertise

Any algebraic question you've got. That includes question that are linear, quadratic, exponential, etc.

Experience

I have solved story problems, linear equations, parabolic equations. I have also solved some 3rd order equations and equations with multiple variables.

Publications
Documents at Boeing in assistance on the manufacturiing floor.

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MS at math OSU in mathematics at OSU, 1986. BS at OSU in mathematical sciences (math, statistics, computer science), 1984.

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Both my BS and MS degrees were given with honors.

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Students in a wide variety of areas since the 80's; over 1,000 of them have been in algebra.