Representation as a product - Examples, Exercises and Solutions

Factored form of the quadratic function

This form is called factored because it uses the factors of a multiplication.

With this form, we can easily identify the points of intersection of the function with the XX axis.
The factored form of the quadratic function looks like this:
y=(xt)×(xk)y=(x-t) \times (x-k)

Suggested Topics to Practice in Advance

  1. Standard Form of the Quadratic Function

Practice Representation as a product

Exercise #1

Determine the points of intersection of the function

y=(x5)(x+5) y=(x-5)(x+5)

With the X

Video Solution

Step-by-Step Solution

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!

Answer

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

Exercise #2

Find the standard representation of the following function

f(x)=(x2)(x+5) f(x)=(x-2)(x+5)

Video Solution

Answer

f(x)+x2+3x10 f(x)+x^2+3x-10

Exercise #3

Find the standard representation of the following function

f(x)=(x6)(x2) f(x)=(x-6)(x-2)

Video Solution

Answer

f(x)=x28x+12 f(x)=x^2-8x+12

Exercise #4

Find the standard representation of the following function

f(x)=(x+2)(x4) f(x)=(x+2)(x-4)

Video Solution

Answer

f(x)=x22x8 f(x)=x^2-2x-8

Exercise #5

Find the standard representation of the following function

f(x)=3x(x+4) f(x)=3x(x+4)

Video Solution

Answer

f(x)=3x2+12x f(x)=3x^2+12x

Exercise #1

Find the standard representation of the following function

f(x)=x(x8) f(x)=-x(x-8)

Video Solution

Answer

f(x)=x2+8x f(x)=-x^2+8x

Exercise #2

Find the standard representation of the following function

f(x)=(x+1)(x1) f(x)=(x+1)(x-1)

Video Solution

Answer

f(x)=x21 f(x)=x^2-1

Exercise #3

Find the standard representation of the following function

f(x)=(2x+1)(x2) f(x)=(2x+1)(x-2)

Video Solution

Answer

f(x)=2x23x2 f(x)=2x^2-3x-2

Exercise #4

Find the standard representation of the following function

f(x)=(x+3)(x4) f(x)=(x+3)(-x-4)

Video Solution

Answer

f(x)=x27x12 f(x)=-x^2-7x-12

Exercise #5

Find the representation of the product of the following function

f(x)=x27x+12 f(x)=x^2-7x+12

Video Solution

Answer

(x3)(x4) (x-3)(x-4)

Exercise #1

Find the representation of the product of the following function

f(x)=x22x3 f(x)=x^2-2x-3

Video Solution

Answer

(x3)(x+1) (x-3)(x+1)

Exercise #2

Find the representation of the product of the following function

f(x)=x23x18 f(x)=x^2-3x-18

Video Solution

Answer

(x6)(x+3) (x-6)(x+3)

Exercise #3

Find the representation of the product of the following function

f(x)=x2+x2 f(x)=x^2+x-2

Video Solution

Answer

(x+2)(x1) (x+2)(x-1)

Exercise #4

Determine the points of intersection of the function

y=(x3)(x+3) y=(x-3)(x+3)

With the X

Video Solution

Answer

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

Exercise #5

Determine the points of intersection of the function

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

With the X

Video Solution

Answer

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

Topics learned in later sections

  1. Ways to represent a quadratic function
  2. Vertex form of the quadratic equation