Question

Write an equation for the parabola with the vertex at (-4,3) that passes through the point (-3,6).

a) y = -x^2 - 7x + 16
b) y = x^2 + 8x + 13
c) y = -x^2 + 5x + 7
d) y = x^2 - 7x + 19

Answer 1

The equation for the parabola with the vertex at (-4,3) that passes through the point (-3,6) is y = (x+4)^2 + 3.

Step-by-step explanation:

The equation for a parabola with the vertex at (-4,3) can be represented in the form y = a(x-h)^2 + k, where (h,k) is the vertex. Substituting the given vertex values, we have y = a(x+4)^2 + 3. To find the value of a, we can substitute the coordinates of the given point (-3,6) into the equation. So, 6 = a(-3+4)^2 + 3. Solving this equation, we get a = 1. Therefore, the equation for the parabola is y = (x+4)^2 + 3.