How to write the vertex form of a quadration that has the vertex of (3,3) and passes through the point (5,11)?

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30-05-2018
Mathematics

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How to write the vertex form of a quadration that has the vertex of (3,3) and passes through the point (5,11)?

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altavistard altavistard · Answer 1 · 2018-06-06T18:32:47+02:00

"quadration?" "quadratic equation?"

Write out the general vertex form and then plug in the given info:

y = a(x-h)^2 + k

Vertex at (3,3): y = a(x-3)^2 + 3

curve passes thru (5,11): 11 = a(5-3)^2 + 3
11 = a(2)^2 + 3 = 4a + 3 = 11, or a = 2

Then the equation of this parabola is

y = 2(x-3)^2 + 3.

check: Does this pass thru (5,11)? Is 11 = 2(5-3)^2 + 3 true?
Is 11 = 2(4)+3 true? YES