Question

What is the equation in vertex form of a parabola with a vertex of (-3,4) that passes through the point (1,-4).

a) y = 1/2(x+3)^2-4
b) y = -1/2(x-3)^2-4
c) y = -1/2(x+3)^2+4
d) y = -2(x+3)^2-4

Answer 1

The equation in vertex form of a parabola with a vertex of (-3,4) that passes through the point (1,-4) is y = -1/2(x+3)^2 + 4.

Step-by-step explanation:

The equation in vertex form of a parabola with a vertex of (-3,4) that passes through the point (1,-4) can be found using the formula y = a(x-h)^2 + k, where (h,k) is the vertex of the parabola.

First, substitute the coordinates of the vertex into the equation: y = a(x+3)^2 + 4.

Next, substitute the coordinates of the given point into the equation and solve for a. Using (1,-4), we get -4 = a(1+3)^2 + 4, which simplifies to -4 = 16a + 4. Solving for a, we find a = -1/2.

Finally, substitute the value of a into the equation and simplify: y = -1/2(x+3)^2 + 4.