Zero points of a function are its intersection points with the $X$-axis.

To find them, we set $Y=0$,

we get an equation that can sometimes be solved using a trinomial or the quadratic formula.

Zero points of a function are its intersection points with the $X$-axis.

To find them, we set $Y=0$,

we get an equation that can sometimes be solved using a trinomial or the quadratic formula.

**Two results -**

In this case, the function intersects the $X$-axis at two different points.**One result -**

In this case, the function intersects the $X$-axis at only one point, meaning the vertex of the parabola is exactly on the $X$-axis.**No results -**

In this case, the function does not intersect the $X$-axis at all, meaning it hovers above or below it.

Question 1

Determine the points of intersection of the function

\( y=(x-5)(x+5) \)

With the X

Question 2

Determine the points of intersection of the function

\( y=x(-x-1) \)

With the X

Question 3

Determine the points of intersection of the function

\( y=(4x+8)(x+1) \)

With the X

Question 4

Determine the points of intersection of the function

\( y=x(x+5) \)

With the X

Question 5

Consider the following function:

\( y=x(x-1) \)

Determine the points of intersection with x.

Determine the points of intersection of the function

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

With the X

To find the point of intersection with the X-axis, we will want to establish that Y=0.

0 = (x-5)(x+5)

When we have an equation of this type, we know that one of these parentheses must be equal to 0, so we will check the possibilities.

x-5 = 0

x = 5

x+5 = 0

x = -5

That is, we have two points of intersection with the x-axis, when we discover their x points, and the y point is already known to us (0, as we placed it):

(5,0)(-5,0)

This is the solution!

$(5,0),(-5,0)$

Determine the points of intersection of the function

$y=x(-x-1)$

With the X

$(-1,0),(0,0)$

Determine the points of intersection of the function

$y=(4x+8)(x+1)$

With the X

$(-1,0),(-2,0)$

Determine the points of intersection of the function

$y=x(x+5)$

With the X

$(-5,0),(0,0)$

Consider the following function:

$y=x(x-1)$

Determine the points of intersection with x.

$(0,0),(1,0)$

Question 1

Determine the points of intersection of the function

\( y=(x-1)(x+10) \)

With the X

Question 2

Determine the points of intersection of the function

\( y=(x+7)(x+2) \)

With the X

Question 3

Determine the points of intersection of the function

\( y=(x-1)(x-1) \)

With the X

Question 4

Determine the points of intersection of the function

\( y=(x-11)(x+1) \)

With the X

Question 5

Determine the points of intersection of the function

\( y=(x+3)(x-3) \)

With the X

Determine the points of intersection of the function

$y=(x-1)(x+10)$

With the X

$(1,0),(-10,0)$

Determine the points of intersection of the function

$y=(x+7)(x+2)$

With the X

$(-2,0),(-7,0)$

Determine the points of intersection of the function

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

With the X

$(1,0)$

Determine the points of intersection of the function

$y=(x-11)(x+1)$

With the X

$(-1,0),(11,0)$

Determine the points of intersection of the function

$y=(x+3)(x-3)$

With the X

$(3,0),(-3,0)$

Question 1

Determine the points of intersection of the function

\( y=(x-2)(x+3) \)

With the X

Question 2

Determine the points of intersection of the function

\( y=(x-3)(x+3) \)

With the X

Question 3

Determine the points of intersection of the function

\( y=(x+8)(x-9) \)

With the X

Question 4

Determine the points of intersection of the function

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

With the X

Question 5

Determine the points of intersection of the function

\( y=x(x+1) \)

With the X

Determine the points of intersection of the function

$y=(x-2)(x+3)$

With the X

$(-3,0),(2,0)$

Determine the points of intersection of the function

$y=(x-3)(x+3)$

With the X

$(-3,0),(3,0)$

Determine the points of intersection of the function

$y=(x+8)(x-9)$

With the X

$(-8,0),(9,0)$

Determine the points of intersection of the function

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

With the X

$(6,0),(5,0)$

Determine the points of intersection of the function

$y=x(x+1)$

With the X

$(-1,0),(0,0)$