# Zeros of a Fuction - Examples, Exercises and Solutions

## Finding the zeros of a quadratic function of the form $$y=ax^2+bx+c$$

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.

### When trying to find the zero point, you can encounter three possible results:

1. Two results -
In this case, the function intersects the $X$-axis at two different points.
2. 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.
In this case, the function does not intersect the $X$-axis at all, meaning it hovers above or below it.

## Examples with solutions for Zeros of a Fuction

### Exercise #1

Determine the points of intersection of the function

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

With the X

### Step-by-Step Solution

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!

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

### Exercise #2

The following function has been graphed below:

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

Calculate points A and B.

### Video Solution

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

### Exercise #3

The following function has been graphed below:

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

Calculate points A and B.

### Video Solution

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

### Exercise #4

The following function has been graphed below:

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

Calculate point A.

### Video Solution

$(0,16)$

### Exercise #5

The following function has been graphed below:

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

Calculate points A and B.



### Video Solution

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

### Exercise #6

The following function has been graphed below:

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

Calculate point C.

### Video Solution

$(4,0)$

### Exercise #7

The following function has been graphed below:

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

Calculate points A and B.

### Video Solution

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

### Exercise #8

The following function has been graphed below:

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

Calculate points A and B.

### Video Solution

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

### Exercise #9

Determine the points of intersection of the function

$y=x(-x-1)$

With the X

### Video Solution

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

### Exercise #10

Determine the points of intersection of the function

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

With the X

### Video Solution

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

### Exercise #11

The following function has been graphed below:

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

Calculate point C.

### Video Solution

$(0,5)$

### Exercise #12

Determine the points of intersection of the function

$y=x(x+5)$

With the X

### Video Solution

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

### Exercise #13

Consider the following function:

$y=x(x-1)$

Determine the points of intersection with x.

### Video Solution

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

### Exercise #14

Determine the points of intersection of the function

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

With the X

### Video Solution

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

### Exercise #15

Determine the points of intersection of the function

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

With the X

### Video Solution

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