Final answer:
To determine the equation of a parabola, you need the vertex and a point on the parabola. There are four different forms of the equation: vertex form, standard form, focus-directrix form, and axis of symmetry form. To find the equation using the vertex and point, you can use the vertex form or the standard form.
Step-by-step explanation:
To determine the equation of a parabola, you need the vertex and a point on the parabola. Let's assume the vertex coordinates are (h, k) and the coordinates of the point on the parabola are (x1, y1). There are different forms for the equation of a parabola:
A: Vertex Form: y = a(x - h)² + k
B: Standard Form: y = ax² + bx + c
C: Focus-Directrix Form: (x - h)² = 4p(y - k)
D: Axis of Symmetry Form: x = h
To determine the equation using the vertex and point, we can use the vertex form or the standard form. With the vertex form, substitute the values of the vertex coordinates and the point coordinates into the equation and solve for a. With the standard form, substitute the values of the point coordinates into the equation and solve for a, b, and c.