How do you find the equation of a parabola, vertex is (2,20) and the x-intercept (5,0)?

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Answer 1 · 2016-01-08T01:30:45

Since the problem provides the vertex, start with the vertex form equation for a parabola ...

#y=a(x-h)^2+k#

where, vertex #=(h,k)#

Using the data from the problem ...

#y=a(x-2)^2+20#

Next, solve for #a# using the point (5,0) ...

#0=a(5-2)^2+20=9a+20#

#9a=-20#

#a=-20/9#

Finally, write the complete equation for the parabola ...

#y=(-20/9)(x-2)^2+20#

hope that helped

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