Question 808869: A parabola has a axis of symmetry x=2 and passes through the points (0,7) and (-1,-3) what is its equation?
Answer by solver91311(24713)   (Show Source):
You can put this solution on YOUR website!
In order to find the equation of a parabola, you need at least 3 points on the parabola. We are given 2 points. However, because of symmetry, we know that there is a point with a function value of 7 equidistant from the axis of symmetry x = 2 on the horizontal line y = 7. So we have a third point (4,7) -- since (0,7) is 2 distant from x = 2, we need a point 2 units on the other side, namely (4,7).
Note that we could also have chosen the point (-5,-3) and achieved the same result.
The equation of a general quadratic function is:
\ =\ ax^2\ +\ bx\ +\ c)
So if the function value is 7 when x = 0, which is what the point (0,7) means, then
^2\ +\ b(0)^2\ +\ c\ = 7)
Hence, 
Also, since the point (-1,-3) is on the graph,
^2\ +\ b(-1)\ +\ c\ =\ -3)
But since we know that , we can say:
And since the point (4,7) is on the graph,
^2\ +\ b(4)\ +\ c\ =\ 7)
But since we know that , we can say:
Now all you have to do is to solve the 2X2 system:
and then once you know the values of a and b to go along with the value of c you already know, you can make the substitutions into
and you will have your desired function.
John
Egw to Beta kai to Sigma
My calculator said it, I believe it, that settles it
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