Find the equation of the parabola in which the vertex is at (-3,3), axis parallel to x-axis and passing through the point (1,7).

Answer 1

The equation will be x = A(y-3)² - 3.

This is the vertex form when the axis of the parabola is parallel to the x-axis rather than the more familiar one when the axis is parallel to the y-axis.

You determine A by substituting the point (1,7)...which I will leave to you.

Answer 2

The vertex form is a (x-h)² + k where (h,k) is the vertex

The vertex is at -3, 3 so h=-3. k = 3, so y = a (x+3)² + 3

When x = 1, y=7 so using these you can find a