Calculate Points A and B for the Quadratic Graph of f(x) = x² - 3x - 4

The following function has been graphed below:

$f(x)=x^2-3x-4$

Calculate points A and B.

To solve for points A and B, we find the x-intercepts of the function by setting:

$f(x) = x^2 - 3x - 4 = 0$

We check if it can be factored:

Factor $x^2 - 3x - 4$. The factors of -4 that add to -3 are -4 and 1.

Thus, factor the function as $(x - 4)(x + 1) = 0$.

Set each factor to zero:

• $x - 4 = 0$ implies $x = 4$
• $x + 1 = 0$ implies $x = -1$

These are the x-intercepts, or roots, of the quadratic function.

Therefore, the coordinates of points A and B, where the function intersects the x-axis, are $A(-1, 0)$ and $B(4, 0)$.

The correct choice corresponding to these points is option 3: $A(-1,0), B(4,0)$.

Thus, the solution to the problem is $A(-1,0), B(4,0)$.