General form for vertex form is:
y = a(x - h)² + k
Where the vertex is the point (h, k). We know this to be (5, -3), so we can substitute the values for h and k to get:
y = a(x - 5)² - 3
We then also have another point (6, 1) that gives us an x and y. Substitute those in to leave one unknown which we can solve for:
1 = a(6 - 5)² - 3
1 = a(1)² - 3
1 = a(1) - 3
1 = a - 3
4 = a
So the equation of this parabola in vertex form is:
y = 4(x - 5)² - 3
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