What is the equation of the parabola that has a vertex at # (5, -6) # and passes through point # (31,-9) #?

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Answer 1 · 2016-05-11T23:28:14

For a question of this type, we will use vertex form, #y = a(x - p)^2 + q#

In vertex form, the vertex is at the point #(p, q)#.

#(x, y)# is a point on the graph of the function.

Therefore, we can state that #-9 = a(31 - 5)^2 - 6#, where a influences the breadth and the direction of opening of the parabola.

Solving for a:

#-9 = 676a - 6#

#-9 + 6 = 26a#

#-3/676 = a#

Therefore, the equation of the parabola is #y = -3/676(x- 5)^2 - 6#

Hopefully this helps!