Write the quadratic equation that has a Vertex at -4, negative 1 includes the point -2, 1

y = (1/2)(x + 4)^2 - 1

Explanation:

Start with the general quadratic equation in vertex form:
y = a(x - h)^2 + k

The vertex is at (h, k).
* Remember that -h is shown in the equation.

Substitute the information from the question into the general equation.
x = -2
y = 1
h = -4
k = -1

y = a(x - h)^2 + k
1 = a(-2 - (-4))^2 + (-1)

Simplify and isolate “a”
1 = a(-2 + 4)^2 - 1
1 = a(2)^2 - 1
1 = 4a - 1
4a = 2
a = 2/4
a = 1/2

Rewrite the general equation with values for “a”, “h” and “k”.
y = a(x - h)^2 + k
y = (1/2)(x + 4)^2 – 1