Question

What is the equation of the parabola given the vertex and focus?

a) y = (x - 0)^2 + 1
b) y = (x - 0)^2 + 2.5
c) y = (x - 0)^2 - 1
d) y = (x - 0)^2 - 2.5

Answer 1

The equation of the parabola given the vertex and focus is y = x^2

Step-by-step explanation:

The equation of a parabola can be determined using the vertex and focus of the parabola. The general equation of a parabola is y = ax^2 + bx + c. To find the values of a, b, and c, we need to use the vertex and focus coordinates.

Let's assume the vertex is (h, k) and the focus is (h + p, k). Since the focus is one unit above the vertex, we have k + 1 as the y-coordinate of the focus.

In this case, the vertex is (0, 0) and the focus is (0, 1). The equation of the parabola would be y = (x - 0)^2 + 0, which simplifies to y = x^2.