SOLUTION: A parabola's vertex is at the point (10,0). If this parabola passes through the point (8,4), where must it cross the y-axis?

SOLUTION: A parabola's vertex is at the point (10,0). If this parabola passes through the point (8,4), where must it cross the y-axis?

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Question 352781: A parabola's vertex is at the point (10,0). If this parabola passes through the point (8,4), where must it cross the y-axis?
Answer by solver91311(24713) (Show Source): You can put this solution on YOUR website!

First thing: Since the value of the function for the given point is greater than the value of the function at the vertex, the parabola must open upwards.

Second thing: By symmetry, since the parabola passes through (8,4) it must also pass through (12,4). (the

-value 8 is 2 smaller than the

-value of the vertex, so the point with an

-value 2 larger than the

-value of the vertex must also have a function value of 4.)

Now we have three points and can determine the coefficients of the quadratic function.

We have a quadradic function of the form:

And three points on the graph of our function, (10,0), (8,4), and (12,4).

Considering the first point:

which is to say:

Likewise, from the coordinates of the other two points we can derive:

And

Since

has a

-intercept at

, all you need to do is solve the system of equations to determine the value of

John

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