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Sagot :
The equation of the parabola is y = 5(x -2)^2 - 3
How to determine the equation of the parabola?
A parabola is represented as:
y = a(x -h)^2 + k
It has its vertex at (2,-3).
This means that
(h,k) = (2,-3)
So, we have:
y = a(x -2)^2 - 3
It has its y-intercept at 5.
This means that
(x,y) = (0,5)
So, we have:
5 = a(0 -2)^2 - 3
Evaluate
5 = 4a - 3
Add 3 to both sides
4a = 8
Divide both sides by 4
a = 2
Substitute a = 2 in y = a(x -2)^2 - 3
y = 5(x -2)^2 - 3
Hence, the equation of the parabola is y = 5(x -2)^2 - 3
Read more about parabola at:
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