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Hey, my teacher is giving us past papers as H.W. and I was wondering if anyone knew how to solve this one. Im kind of stuck.

g is a quadratic function where g(0)=5. Its symmetry axis is x=2. Find the equation of g expressed as a(x-h)"2 +3


Edited by Amy0501

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Recognize that an untransformed quadratic function has symmetry on x = 0. x = 2 symmetry means the graph is horizontally shifted 2 units to the right. That means h = 2. 

g(0) = 5 is point on the curve. g(0) = a(0 - h)2 + 3 = a(0 - 2)2 + 3 = 4a + 3 = 5 ==> 4a = 2, a = 1/2

EDIT: formal answer would be g(x) = 1/2 * (x - 2)2 + 3

One way to visualize the solution is to understand as it stands, both a and h are unknown so you need some separate information for solve for each. So one thing to practise is converting the written information (symmetry axis is x = 2) to a mathematical one (horizontal shift is 2 units to the right). 


Edited by kw0573

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