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.

Question Types:

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

The following function has been graphed below:

\( f(x)=-x^2+5x+6 \)

Calculate points A and B.

Question 3

The following function has been graphed below:

\( f(x)=x^2-6x+8 \)

Calculate points A and B.

Question 4

The following function has been graphed below:

\( f(x)=x^2-8x+16 \)

Calculate point A.

Question 5

The following function has been graphed below:

\( f(x)=x^2-6x+5 \)

Calculate points A and B.

\( \)

Determine the points of intersection of the function

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

With the X

In order to find the point of the intersection with the X-axis, we first need 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 begin by checking the possible options.

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!

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

The following function has been graphed below:

$f(x)=-x^2+5x+6$

Calculate points A and B.

$(-1,0),(6,0)$

The following function has been graphed below:

$f(x)=x^2-6x+8$

Calculate points A and B.

$(2,0),(4,0)$

The following function has been graphed below:

$f(x)=x^2-8x+16$

Calculate point A.

$(0,16)$

The following function has been graphed below:

$f(x)=x^2-6x+5$

Calculate points A and B.

$(1,0),(5,0)$

Question 1

The following function has been graphed below:

\( f(x)=x^2-8x+16 \)

Calculate point C.

Question 2

The following function has been graphed below:

\( f(x)=x^2-6x \)

Calculate points A and B.

Question 3

The following function has been graphed below:

\( f(x)=x^2-3x-4 \)

Calculate points A and B.

Question 4

Determine the points of intersection of the function

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

With the X

Question 5

Determine the points of intersection of the function

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

With the X

The following function has been graphed below:

$f(x)=x^2-8x+16$

Calculate point C.

$(4,0)$

The following function has been graphed below:

$f(x)=x^2-6x$

Calculate points A and B.

$(6,0),\lparen0,0)$

The following function has been graphed below:

$f(x)=x^2-3x-4$

Calculate points A and B.

$A(-1,0),B(4,0)$

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

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

Question 1

The following function has been graphed below:

\( f(x)=x^2-6x+5 \)

Calculate point C.

Question 2

Determine the points of intersection of the function

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

With the X

Question 3

Consider the following function:

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

Determine the points of intersection with x.

Question 4

Determine the points of intersection of the function

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

With the X

Question 5

Determine the points of intersection of the function

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

With the X

The following function has been graphed below:

$f(x)=x^2-6x+5$

Calculate point C.

$(0,5)$

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.

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

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

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