Find the Intersection Points: Solve the Quadratic y=(4x+8)(x+1)

To solve this problem, we'll follow these steps:

• Step 1: Set the function $y = (4x + 8)(x + 1)$ equal to zero, i.e., $(4x + 8)(x + 1) = 0$.
• Step 2: Apply the zero-product property to resulting factors.
• Step 3: Solve each equation for $x$.

Now, let's work through each step:
Step 1: We start by setting the equation to zero:
$(4x + 8)(x + 1) = 0$.

Step 2: Using the zero-product property, we find:
1. $4x + 8 = 0$
2. $x + 1 = 0$

Step 3: Solve each of these equations for $x$:

For $4x + 8 = 0$, subtract 8 from both sides to get $4x = -8$. Divide both sides by 4, resulting in:
$x = -2$.

For $x + 1 = 0$, subtract 1 from both sides to get:
$x = -1$.

Thus, the points of intersection of the function with the x-axis are the solutions we just found. At these points, the y-value is zero, giving us the intersection points as $(-1, 0)$ and $(-2, 0)$.

Therefore, the solution to the problem is $(-1, 0), (-2, 0)$.