Question 524747: each point lies on a parabola that has its vertex at (0,1) write the equation of the parabola. Indicate whether the graph opens up or down. (-1,6)
Answer by solver91311(24713)   (Show Source):
You can put this solution on YOUR website!
Since the vertex is on the  -axis, symmetry says that if ) is on the parabola, ) is on the parabola. Now that we have three points on the parabola we can write the equation.
All parabolas with a vertical axis of symmetry can be described by a function of the form:
\ =\ ax^2\ +\ bx\ +\ c)
So, if the point ) is on the parabola, then
^2\ +\ b(0)\ +\ c\ =\ 1)
Then, if the point ) is on the parabola, then
^2\ +\ b(-1)\ +\ c\ =\ 6)
Then, if the point is on the parabola, then
^2\ +\ b(1)\ +\ c\ =\ 6)
Substituting the known value of  we are left with a 2X2 system:
And then substituting the now known coefficients into the function definition:
\ =\ 5x^2\ +\ 1)
Since the lead coefficient is positive, the parabola opens upward.
John
My calculator said it, I believe it, that settles it
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