Finding Points A and B on the Quadratic Graph of f(x) = -x^2 + 5x + 6

To solve for the x-intercepts of the function $f(x) = -x^2 + 5x + 6$, we will find the roots of the quadratic equation $-x^2 + 5x + 6 = 0$.

Let's attempt to factor this quadratic equation first. Rewrite the equation as follows:

$-x^2 + 5x + 6 = 0$.

To factor, we look for two numbers that multiply to $-6$ (the product of $a$ and $c$, where $a = -1$ and $c = 6$) and add to $5$ (the middle coefficient $b$).

The numbers that satisfy this condition are $-1$ and $6$.

Thus, the quadratic can be factored as:

$(x - 6)(x + 1) = 0$.

Setting each factor equal to zero gives us:

$x - 6 = 0$ or $x + 1 = 0$.

Solving these equations, we find:

$x = 6$ and $x = -1$.

Thus, the points A and B, the x-intercepts of the function, are:

$(-1, 0)$ and $(6, 0)$.

Therefore, the solution to the problem is $(-1, 0), (6, 0)$.