SOLUTION: Write the equation of a quadratic function in vertex form with a vertex at(0,5) and contains the point(1,-2)?

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Question 1155562: Write the equation of a quadratic function in vertex form with a vertex at(0,5) and contains the point(1,-2)?
Answer by greenestamps(13198) About Me  (Show Source):
You can put this solution on YOUR website!


With the vertex on the y-axis at (0,5), the equation is of the form

y+=+ax%5E2%2B5

To find the coefficient a and thus find the equation, plug in the coordinates of the other given point.

-2+=+a%281%5E2%29%2B5
-2+=+a%2B5
a+=+-7

The equation is y+=+-7x%5E2%2B5

There is another less formal method for finding the coefficient a which you can use if you understand parabolas and quadratic functions. The equation

y+=+ax%5E2%2B5

tells you that the displacement in y is a times the displacement in x. From (0,5) to (1,-2) the displacement in x is 1; the square of that is 1. And the corresponding displacement in y is -7; -7 is -7 times 1, so a is -7.