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

Question

Determine the points of intersection of the function

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

With the X

00:00 Find the intersection points with the X-axis

00:03 At the intersection point with the X-axis, the Y value must = 0

00:07 Set Y = 0 and solve to find X values

00:13 Find what zeroes each factor in the multiplication

00:32 This is one solution

00:57 This is the second solution

01:10 Let's verify that each solution truly zeroes the Y value

01:36 This solution zeroes

01:50 Let's check the second solution

02:15 This solution also zeroes, these are the intersection points with the X-axis

02:24 And this is the solution to the question

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:

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 $(1, 0)$ .

$(-\frac{1}{2},0),(1,0)$