Determining the Quadratic Function with a Vertex at (2, -9) | Analyzing Given Functions and Comparing to Vertex Form

Which function has a vertex at (2, -9)?f(x) = -(x – 3)2f(x) = (x + 8)2f(x) = (x – 5)(x + 1)f(x) = -(x – 1)(x – 5)

To find the function that has a vertex at (2, -9), we need to recall the vertex form of a quadratic function, which is:

f(x) = a(x – h)^2 + k

Where (h, k) represents the coordinates of the vertex

To find the function that has a vertex at (2, -9), we need to recall the vertex form of a quadratic function, which is:

f(x) = a(x – h)^2 + k

Where (h, k) represents the coordinates of the vertex. In this case, h = 2 and k = -9.

Now let’s examine each given function to see which one matches the vertex form:

1. f(x) = -(x – 3)^2

Comparing this with the vertex form, we notice that h = 3, not 2. Therefore, this function does not have a vertex at (2, -9).

2. f(x) = (x + 8)^2

Again, h here is -8, not 2. Hence, this function does not have a vertex at (2, -9).

3. f(x) = (x – 5)(x + 1)

This is not a vertex form of the quadratic function. It’s actually a factored form (or expanded form) of a quadratic equation. It represents a parabola but does not have a vertex at (2, -9).

4. f(x) = -(x – 1)(x – 5)

Comparing this with the vertex form, we can see that h = (1+5)/2 = 6/2 = 3, which does not match the given x-coordinate of the vertex, 2. Therefore, this function does not have a vertex at (2, -9) either.

Hence, none of the given functions match the vertex (2, -9). It’s possible that there was a typographical error or some missing information.

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