Which of the following functions best describes this graph?

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Question:

Which of the following functions best describes this graph?

Answer:

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:

  • The arms of the graph open upwards, so the leading coefficient is positive.
  • The y-intercept seems to be larger than 10.
  • The vertex has a positive x-value and a negative y-value.

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.

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C) y = x^2 – 9x + 18

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.

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