Write the equation for parbola in vertex form

Vertex: (-4,6); Point: (-2,-2)

f (x) = a(x - h)2 + k, where (h, k) is the vertex

-2 = a (-2 - -4) + 6 ... a = -4

y = -4 (x + 4) + 6

Alright, here's the equation for the parabola in vertex form:

(y - 6) = a(x + 4)^2

Now we just need to find the value of 'a'. To do that, let's substitute the given point (-2, -2) into the equation:

(-2 - 6) = a(-2 + 4)^2
-8 = a(2)^2
-8 = 4a

Now, let's solve for 'a':

-8/4 = a
-2 = a

Therefore, the equation for the parabola in vertex form is:

(y - 6) = -2(x + 4)^2

Hope that answers your question, and remember, life can sometimes be a parabola - it has its ups and downs!

To write the equation of a parabola in vertex form, the general vertex form equation is:

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

Where (h, k) represents the vertex of the parabola. We can use the given information to find the values of h, k, and a.

Given: Vertex (-4,6) and Point (-2,-2)

Step 1: Determine the vertex values (h, k)
The vertex is given as (-4,6), so h = -4 and k = 6.

Step 2: Substitute the vertex values into the vertex form equation
y = a(x-h)^2 + k
y = a(x - (-4))^2 + 6
y = a(x + 4)^2 + 6

Step 3: Use the point (-2,-2) to solve for a
Substitute x = -2 and y = -2 into the equation:
-2 = a(-2 + 4)^2 + 6
-2 = a(2)^2 + 6
-2 = 4a + 6
4a = -2 - 6
4a = -8
a = -8/4
a = -2

Step 4: Substitute the value of a back into the equation
y = a(x + 4)^2 + 6
y = -2(x + 4)^2 + 6

Therefore, the equation of the parabola in vertex form is:
y = -2(x + 4)^2 + 6

To write the equation for a parabola in vertex form, we can start with the general equation for a parabola:

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

Where (h, k) represents the vertex of the parabola. In this case, the vertex is given as (-4, 6), so we have:

y = a(x - (-4))^2 + 6

which simplifies to:

y = a(x + 4)^2 + 6

Now, we need to find the value of 'a'. To do this, we'll use the point (-2, -2) on the parabola. We substitute these coordinates into the equation:

-2 = a((-2) + 4)^2 + 6

Simplifying further:

-2 = a(2)^2 + 6
-2 = 4a + 6
-8 = 4a
a = -8/4
a = -2

Finally, we substitute the value of 'a' back into the equation:

y = -2(x + 4)^2 + 6

Therefore, the equation for the parabola in vertex form is:

y = -2(x + 4)^2 + 6