The only graph that represents the graph of f(x) = x³ - x² - 6x is;
Graph 1
We are given the function; f(x) = x³ - x² - 6x
Now, we are given 3 graphs to find which one represents the function above.
Let us first find the roots of the quadratic equation by the quadratic equation formula;
x = [-b ± √(b² - 4ac)]/2a
x = [-(-1) ± √(-1² - 4(1 × - 6))]/(2 * 1)
x =( 1 ± √25)/2
x = (5 + 1)/2 or (1 - 5)/2
x = 3 or -2
Now, these roots are the x-intercepts which is the point on the graph where the curve touches the x-axis.
The only graph that has these intercepts is Graph 1.
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