Calculate Points A and B on the Quadratic Graph of x² - 6x + 8

To solve the problem of finding points A and B on the graph of the function $f(x) = x^2 - 6x + 8$, we need to determine where this quadratic function equals zero.

Step-by-step Approach:

• Step 1: Check Factoring Possibility
  The quadratic function is given by:

$f(x) = x^2 - 6x + 8$

We will attempt to factor this quadratic expression. We are looking for two numbers that multiply to the constant term, 8, and add to the coefficient of $x$, which is $-6$.

• Step 2: Identify Factors
  The numbers $4$ and $2$ multiply to $8$ and add to $-6$, if we consider their negative counterparts, $-4$ and $-2$:

$(x - 4)(x - 2) = x^2 - 6x + 8$

This matches our expression, confirming that it is the correct factorization.

• Step 3: Solve for Roots
  Set each factor equal to zero:

$x - 4 = 0 \quad \Rightarrow \quad x = 4$ $x - 2 = 0 \quad \Rightarrow \quad x = 2$

Thus, the points where the function intersects the x-axis, which are the roots, are $(2,0)$ and $(4,0)$.

Therefore, the solution to the problem is that points A and B are at $(2,0)$ and $(4,0)$.

Final Solution:
The points A and B are $(2,0)$ and $(4,0)$.