Find the X-Intercepts: Solving the Quadratic Equation x² - 6x + 5

The following function has been graphed below:

$f(x)=x^2-6x+5$

Calculate points A and B.

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To solve for the points A and B, we need to find the roots of the function $f(x) = x^2 - 6x + 5$ where $f(x) = 0$.

Let's proceed step-by-step:

• Step 1: Set the function to zero
  We begin by setting the equation to zero: $x^2 - 6x + 5 = 0$.
• Step 2: Factor the quadratic
  We need to factor the expression. We look for two numbers that multiply to $c = 5$ and add to $b = -6$. These numbers are $-1$ and $-5$.
• Step 3: Write the factorization
  Therefore, we can write the quadratic as: $(x - 1)(x - 5) = 0$.
• Step 4: Solve for the roots
  Set each factor equal to zero: \begin{align*} x - 1 &= 0 \\ x &= 1 \end{align*} \begin{align*} x - 5 &= 0 \\ x &= 5 \end{align*} The roots are $x = 1$ and $x = 5$.
• Step 5: Identify the Points A and B
  The points A and B, where the function intersects the x-axis, are $(1, 0)$ and $(5, 0)$.

Thus, the coordinates of points A and B are $(1,0),(5,0)$, which matches choice 1.