Which of the following functions best describes this graph?

We want to see which one of the given functions describes the given graph.

The correct option is C:

y = x^2 - 9x + 18

We have a graph of a quadratic equation, the things we can see of the graph are:

From, the second one, we can discard option D, because its y-intercept is smaller than 10, and option A because it has a negative y-intercept.

Now remember that for a general quadratic equation:

y = a*x^2 + b*x + c

the x-value of the vertex is:

x = -b/2a

Now we can compute the x-value of the vertexes of the 2 remaining options.

B) y = x^2 + 9x + 18

Then the x-value of the vertex is:

x  = -9/(2*1) = -4.5

But in the graph we can see that the x-value of the vertex is positive, so we can discard this option.

C) y = x^2 - 9x + 18

Then the x-value of the vertex is:

x = -(-9)/(2*1) = 4.5

In this case, we got a positive x-value for the vertex, as expected.

Because of this (and because we discarded the other 3 options) we can conclude that the function that best describes the graph is the one in option C.

If you want to learn more, you can read:

link

C

Step-by-step explanation:

If you fill in x=0, you are left with the y intercept. In the picture you can see it must be larger than y=10. This invalidates answer A and D.

The  x-coordinate top of the parabola ax²+bx+c=0 is given by y = -b/2a, so immediately we can see -b has to be positive. This leads you to answer C because -9x implies b=-9, and --9 is positive.

(-5,-28)

i graphed to on desmos.

y= 2x+7

changed to y= 5x +7

as slope is increased from 2 to 5

therefore it would be less steeper

so, option d) is correct