Answer:
Graph represented by option D is the correct choice.
Step-by-step explanation:
We have been equation of a function [tex]f(x)=x^2+x-6[/tex]. 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.
[tex]x^2+3x-2x-6=0[/tex]
[tex]x(x+3)-2(x+3)=0[/tex]
[tex](x+3)(x-2)=0[/tex]
[tex](x+3)=0\text{ or }(x-2)=0[/tex]
[tex]x=-3\text{ or }x=2[/tex]
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.
