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Explore This Summary: \(y=a(x-h)^2+k\)
The vertex of \(y=a(x-h)^2+k\) (where \(a \ne 0\)) is \((h,k)\).
A circus act involves shooting a stunt performer out of a cannon into a pool of water. The performer's height above the ground, \(h\) in metres, is given by \(h=-\dfrac{1}{20}(x-15)^2+18\) where \(x\) is the horizontal distance from the cannon. Determine the maximum height of the stunt performer.
Strategy to Solve
Vertex form: \(h=-\dfrac{1}{20}(x-15)^2+18\)
What about if we haev the following from the script as a call-out box to the right?
Determine the maximum height of the stunt performer.
The motion is given by \(h=-\dfrac{1}{20}(x-15)^2+18\), a parabola that opens down with vertex \((15,18)\).
Since the maximum height is the \(h\)-coordinate of the vertex, the stunt performer's maximum height is \(18\) metres.
Key Question: Why is \((h,k)\) the vertex of \(y=a(x-h)^2+k\)?
Facts:
Consider \(y=-(x+2)^2+6\). Why is the vertex \((-2,6)\)?
We have determined the following about quadratic relations written in vertex form.
An equation written in the form \(y=a(x-h)^2+k\), where \(a \ne 0\), corresponds to a graph of a parabola that
Note that this includes equations of the following forms:
Determine the vertex of \(y= ((((((((((f)*(u))*(l))*(l))*(exp(r)))*(e))*(s))*(s))*(i))*(o))*(n) \)
Enter the vertex as an ordered pair. Example "(3,4)".
The vertex is There appears to be a syntax error in the question bank involving the question field of this question. The following error message may help correct the problem: null