Question

Which of the following options represents the equation of the parabola with a vertex at (1,5) that passes through the point (0, -3) in vertex form?

A) y = (x-1)^2 + 5
B) y = (x+1)^2 + 5
C) y = (x-1)^2 - 5
D) y = (x+1)^2 - 5

Answer 1

The equation of the parabola with a vertex at (1, 5) that passes through the point (0, -3) in vertex form is y = (x - 1)^2 + 5.

Step-by-step explanation:

The equation of a parabola with a vertex at (h, k) in vertex form is y = a(x - h)^2 + k, where (h, k) represents the vertex. To find the equation of the parabola with a vertex at (1, 5) that passes through the point (0, -3), we substitute the given values into the vertex form equation.

By substituting the vertex coordinates (h, k) = (1, 5) and the point coordinates (x, y) = (0, -3) into the equation, we get:

1. x - h = 0 - 1 = -1
2. y - k = -3 - 5 = -8

So, the equation of the parabola is y = (-1)^2 - 8, which simplifies to y = (x - 1)^2 - 8. Therefore, the correct option is A) y = (x - 1)^2 + 5.