Determine Intersection Points of y = (x + 7)(x + 2) with X-Axis

To find the points of intersection, follow these steps:

• Step 1: The function given is $y = (x+7)(x+2)$. We are interested in where this function intersects the x-axis, which occurs when $y = 0$.
• Step 2: Set the function equal to zero: $(x+7)(x+2) = 0$.
• Step 3: Solve for $x$ using the zero-product property, which states that if the product of two factors is zero, then at least one of the factors must be zero.

Now, solve the equation:
Step 1: Set $x+7 = 0$, which gives $x = -7$.
Step 2: Set $x+2 = 0$, which gives $x = -2$.

These values are the $x$-coordinates where the function intersects the x-axis. Since the y-coordinates at each of these points is zero, the intersection points are $(-7,0)$ and $(-2,0)$.

Therefore, the points of intersection are $(-2,0)$ and $(-7,0)$.