Question

What is the equation in vertex form for the function?

The vertex form is (-3, -4) and (-2, -3)

Answer 1

[AI-generated answer — Bot GPT 3.5]

The vertex form of a quadratic function is given by:

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

where (h, k) is the vertex of the parabola.

Using the given vertex points (-3, -4) and (-2, -3), we can plug these values into the equation:

-4 = a(-3 - h)^2 + k
-3 = a(-2 - h)^2 + k

Substitute (-3, -4) into the first equation:

-4 = a(-3 - h)^2 + k
-4 = a(9 + 6h + h^2) + k
-4 = 9a + 6ah + ah^2 + k

Substitute (-2, -3) into the second equation:

-3 = a(-2 - h)^2 + k
-3 = a(4 + 4h + h^2) + k
-3 = 4a + 4ah + ah^2 + k

Now we have a system of equations:

-4 = 9a + 6ah + ah^2 + k
-3 = 4a + 4ah + ah^2 + k

Subtract the second equation from the first equation:

-1 = 5a + 2ah + k

Now we have a system of two equations:

-1 = 5a + 2ah + k
-4 = 9a + 6ah + k

Solve this system of equations to find the value of 'a', 'h', and 'k' to get the vertex form of the function.