college algebra word problem

Question

Use the vertex (h, k) and a point on the graph (x, y) to find the general form of the equation of the quadratic function.

(h, k) = (1, 0), (x, y) = (0, 1)

Answer 1

(0,1) is to the left and above the vertex, You could get 2 different equations, depending on whether the parabola opens upward or to the left

upward would have y=a(x-1)^2 plug in the other point (0,1) to solve for a. 1 =a, so y=(x-1)^2 is the equation, or y= x^2 + 2x + 1

leftward would have x-1 =a(y-0)^2. plug in the other point (0,1) to solve for a. -1 =a, so x-1=-y^2 is the equation or y= +sqr(1-x)

that's the easiest answers. There could be an infinite number of equations with that vertex going through that point, if you include slanted parabolas, with axes of symmetry at angles other than 0, 90, 180 and 270 degrees. They would have xy terms in the equation.