Product Representation: Linking function properties to its representation

Transition between different representations of a function

Question 1

Determine the points of intersection of the function

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

With the X

Question 2

Consider the following function:

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

Determine the points of intersection with 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

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

With the X

Question 5

Determine the points of intersection of the function

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

With the X

Examples with solutions for Product Representation: Linking function properties to its representation

Exercise #1

Determine the points of intersection of the function

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

With the X

Video Solution

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!

Answer

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

Exercise #2

Consider the following function:

$y=x(x-1)$

Determine the points of intersection with x.

Video Solution

Answer

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

Exercise #3

Determine the points of intersection of the function

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

With the X

Video Solution

Answer

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

Exercise #4

Determine the points of intersection of the function

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

With the X

Video Solution

Answer

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

Exercise #5

Determine the points of intersection of the function

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

With the X

Video Solution

Answer

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

Question 1

Determine the points of intersection of the function

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

With the X

Question 2

Determine the points of intersection of the function

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

With the X

Question 3

Determine the points of intersection of the function

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

With the X

Question 4

Determine the points of intersection of the function

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

With the X

Question 5

Determine the points of intersection of the function

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

With the X

Exercise #6

Determine the points of intersection of the function

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

With the X

Video Solution

Answer

$(1,0)$

Exercise #7

Determine the points of intersection of the function

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

With the X

Video Solution

Answer

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

Exercise #8

Determine the points of intersection of the function

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

With the X

Video Solution

Answer

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

Exercise #9

Determine the points of intersection of the function

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

With the X

Video Solution

Answer

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

Exercise #10

Determine the points of intersection of the function

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

With the X

Video Solution

Answer

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

Question 1

Determine the points of intersection of the function

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

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

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

With the X

Question 4

Does the parable

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

Is there a minimum or maximum point?

Question 5

Determine the points of intersection of the function

$$ y=2x(2x+4) $$

With the X

Exercise #11

Determine the points of intersection of the function

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

With the X

Video Solution

Answer

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

Exercise #12

Determine the points of intersection of the function

$y=x(-x-1)$

With the X

Video Solution

Answer

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

Exercise #13

Determine the points of intersection of the function

$y=x(x+5)$

With the X

Video Solution

Answer

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

Exercise #14

Does the parable

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

Is there a minimum or maximum point?

Video Solution

Answer

Minimal point

Exercise #15

Determine the points of intersection of the function

$y=2x(2x+4)$

With the X

Video Solution

Answer

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

Question 1

Determine the points of intersection of the function

$$ y=2x(x-6) $$

With the X

Question 2

Determine the points of intersection of the function

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

With the X

Question 3

Determine the points of intersection of the function

$$ y=(x-2)(x+4) $$

With the X

Question 4

Determine the points of intersection of the function

$$ y=(x-2)(x+4) $$

With the X

Question 5

Determine the points of intersection of the function

$$ y=(x-2)(x+4) $$

With the X

Exercise #16

Determine the points of intersection of the function

$y=2x(x-6)$

With the X

Video Solution

Answer

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

Exercise #17

Determine the points of intersection of the function

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

With the X

Video Solution

Answer

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

Exercise #18

Determine the points of intersection of the function

$y=(x-2)(x+4)$

With the X

Video Solution

Answer

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

Exercise #19

Determine the points of intersection of the function

$y=(x-2)(x+4)$

With the X

Video Solution

Answer

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

Exercise #20

Determine the points of intersection of the function

$y=(x-2)(x+4)$

With the X

Video Solution

Answer

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