Question

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

Answer 1

The last graph represents the function

Answer 2

Graph represented by option D is the correct choice.

Explanation:

We have been equation of a function
`f(x)=x^2+x-6`. 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.

`x^2+3x-2x-6=0`

`x(x+3)-2(x+3)=0`

`(x+3)(x-2)=0`

`(x+3)=0\text{ or }(x-2)=0`

`x=-3\text{ or }x=2`

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.