Question

Find an equation of the parabola that has the indicated vertex and whose graph passes through the given point

Vertex: ( 2, -1) ; point: ( 4, -3)

Answer 1

Equation of a parabola with vertex at (2, -1) is
y = a(x - 2)^2 - 1

Using the given point: -3 = a(4 - 2)^2 - 1
-2 = a(2)^2
4a = -2
a = -1/2

Therefore, required equation is
y = -1/2(x - 2)^2 - 1
y = -1/2(x^2 - 4x + 4) - 1
y = -1/2x^2 + 2x - 2 - 1
y = -1/2x^2 + 2x - 3