Which of the following graphs represents the function f(x) = x2 + x − 6?

Graph represented by option D is the correct choice.

Step-by-step explanation:

We have been equation of a function . We are asked to choose the graph representing this function.

We can see that our given function is a quadratic function, so it will be in form of parabola. Since the leading coefficient is positive, so our parabola will open upwards.

Since a quadratic function can have at-most 2 zeros. Let us find the zeros of our given function by using factoring.

We will factor our given function by splitting the middle term.

So the graph of our given function will intersect x-axis at x=-3 and x=2.

Upon looking at our given choices we can see that graph represented by option A and C intersects x axis at 3 places. The graph represented by option B intersects x-axis at 4 places. So option A, B and C are not correct choices.

Since the graph represented by option D is an upward opening parabola and it intersects x-axis at exactly two places that are x=-3 and x=2, therefore, option D is the correct choice.

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step-by-step explanation:

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