Final answer:
To put the functions in order of smallest maximum value to largest maximum value, we need to analyze the quadratic function and compare the vertex with the given options.
Step-by-step explanation:
To put the functions in order of smallest maximum value to largest maximum value, we need to analyze the function f(x)=-(x-3)^(2)+6. This function is in the form of a quadratic equation, and we can determine its maximum value by finding the vertex.
The vertex form of a quadratic equation is given by f(x) = a(x-h)^2 + k, where (h, k) is the vertex. Comparing this with the given function f(x)=-(x-3)^(2)+6, we can see that h=3 and k=6.
- Let's consider option a. y = 13x.
- Now let's consider option b. y = x².
Comparing the vertex of the given equation (-3, 6) with the graphs of the options, we can conclude that option a has the smallest maximum value, option b has the largest maximum value, and the given function f(x) is between them.