What is the equation of the following graph?

There are a couple of different ways you could do this, but I'll show the simpler way. We will use the formula

along with the fact that the vertex has h and k coordinates of 1 and 4 respectively, and that a point on the graph is (3, 5). We could have used any point on the graph where there is a definite integer coordinate pair. We will fill in accordingly and solve for a.

and

5 = 4a + 4. If we subtract 4 from both sides we get that . Now we will fill in the formula and expand as needed:

and

. If we distribute the 1/4 in and then add the constants the final equation for that graph will be

the required function is .

step-by-step explanation:

from the given table it is noticed that the graph passing through (-3,7), (0,4), (3,1) and (8,-4).

it is a linear function because the value of y is decrease by one as the value of x increase by 1.

the slope of the function is

the slope of the function is -1 and the y-intercept is 4.

the slope intercept form is

where, m is slope and b is y-intercept.

therefore the required function is . the graph of this function is shown below.