Question

The graph of a quadratic function is shown on the grade.

Answer 1

Answer:

C ( h(x) = x^2 - 6x)

Step-by-step explanation:

Assuming that the function has a slope of 1 (none of the answer choices show a different slope, for all of the coefficients of x^2 are 1) the easiest way to solve this problem would be to find the function for the graph instead of inputting points from the graph into each of the function. (you could do that if you weren't sure.) To get a function from the graph, we first have to find the vertex and enter it into this vertex form function:

h(x) = (x - a )^2 - b

(there are other ways, but finding the vertex and putting the function in vertex form and then simplifying is the easiest way in this situation.) Looking at the graph, we can tell that the vertex of the function is (3, -9). Using the fact that h(x) = (x - a )^2 - b works for the vertex (-a, b), we can conclude that the function is

h(x) = (x - 3)^2 - 9.

This is not an answer! We have to simplify (x - 3)^2 - 9 to answer the question.  By squaring x - 3, we get:

x^2 - 6x + 9 - 9 =

x^2 - 6x.

Therefore, the answer is:

C (h(x) = x^2 - 6x).