Question 21 (1 point) This table shows the input and output values for a linear function f(x). What is the positive difference o
f outputs for any two inputs that are four values apart? x −3 −2 −1 0 1 2 3 f(x) −1.5 −1 −0.5 0 0.5 1 1.5 Enter your answer in the box. (Enter the number and nothing else)
2 answers:
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Notice that our function 
is a parabola, and the vertex form of a parabola is:
where (h,k) are the coordinates of its vertex.
The first thing we need to do is find the vertex (h,k) and to do that we are going to use the vertex formula:
, and then we are going to evaluate our function at 
to find 
.
We know for our problem that
, and 
, so lets replace those values in our vertex formula to find :
Now, we are going to evaluate our function at -6 to find:
Now that we have our vertex, where and ; lets replace those values in our vertex form equation:
![f(x)=-5[x-(-6)]^{2} +(-1)](https://tex.z-dn.net/?f=f%28x%29%3D-5%5Bx-%28-6%29%5D%5E%7B2%7D%20%2B%28-1%29)
We can conclude that the vertex form of our function is, and its vertex is (-6,-1).
The first thing we need to do is find the vertex (h,k) and to do that we are going to use the vertex formula:
We know for our problem that
Now, we are going to evaluate our function at -6 to find
Now that we have our vertex, where
We can conclude that the vertex form of our function is