Determine the X-axis Intersection Points of the Quadratic Function: y = (x-1)(2x+1)

Determine the points of intersection of the function

$y=(x-1)(2x+1)$

With the X

To find the points of intersection with the x-axis for the function $y = (x-1)(2x+1)$, we must determine when $y = 0$.

Using the zero-product property, set each factor equal to zero separately:

• $x - 1 = 0$
• $2x + 1 = 0$

Solving the first equation, $x - 1 = 0$:
Add 1 to both sides:
$x = 1$.

Solving the second equation, $2x + 1 = 0$:
Subtract 1 from both sides:
$2x = -1$.
Divide both sides by 2:
$x = -\frac{1}{2}$.

The solutions are the x-intercepts of the function. Therefore, the points of intersection are $(1, 0)$ and $\left(-\frac{1}{2}, 0\right)$.

Thus, the points of intersection on the x-axis are $(- \frac{1}{2}, 0)$ and $(1, 0)$.