The equation of the parabola given in the graph is:
(x - 5)² = -8(y + 4).
What is the equation of a parabola given it’s vertex?
The equation of a quadratic function, of vertex (h,k), is given by:
a(y - k) = (x - h)²
In which a = 4p is the leading coefficient.
In this problem, the vertex is at point (5,-4), hence h = 5, k = -4, and the equation is:
a(y + 4) = (x - 5)²
The focus is at y = -6, which means that p = -6 - (-4) = -2, hence the leading coefficient is:
a = 4p = 4(-2) = -8
Hence the equation is:
(x - 5)² = -8(y + 4).
More can be learned about the equation of a parabola at https://brainly.com/question/24737967
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