Find the X-Intercepts of the Quadratic Function y=(x-6)(x-5)

Determine the points of intersection of the function

$y=(x-6)(x-5)$

With the X

To solve this problem, we'll determine where the graph of the function intersects the x-axis by following these steps:

• Step 1: Set the function equal to zero: $y = (x-6)(x-5) = 0$.
• Step 2: Solve for the x-values where the equation equals zero.
• Step 3: Express these x-values as points where $y$ is zero, representing the intersections with the x-axis.

Now, let's apply these steps:

Step 1: Set the equation to zero: $(x-6)(x-5) = 0$.

Step 2: Solve for $x$.

• Set the first factor to zero: $x-6 = 0$. Solving for $x$ gives $x = 6$.
• Set the second factor to zero: $x-5 = 0$. Solving for $x$ gives $x = 5$.

Step 3: The solutions represent points on the x-axis where the function intersects.

Thus, the points of intersection are $(6, 0)$ and $(5, 0)$.

Therefore, the solution to the problem is $(6,0),(5,0)$.