What is the equation of the parabola that has a vertex at # (4, 4) # and passes through point # (17,-8) #?

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Answer 1 · 2016-06-05T15:53:26

For problems like this, we use vertex form, #y = a(x - p)^2 + q#, where the vertex is at #(p, q)# and the given point is at #(x, y)#

We will be solving for parameter #a# in vertex form, which influences the direction of opening and the breadth of the parabola.

#-8 = a(17 - 4)^2 + 4#

#-12 = a(13)^2#

#-12 = 169a#

#-12/169 = a#

The equation of the parabola is therefore #y = -12/169(x - 4)^2 + 4#

Hopefully this helps!