Representation as a product - Examples, Exercises and Solutions

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!

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

Find the standard representation of the following function

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

$f(x)+x^2+3x-10$

Find the standard representation of the following function

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

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

Find the standard representation of the following function

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

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

Find the standard representation of the following function

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

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

Find the standard representation of the following function

$f(x)=-x(x-8)$

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

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

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

With the X

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

Does the parable

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

Is there a minimum or maximum point?

Minimal point

Find the standard representation of the following function

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

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

Find the standard representation of the following function

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

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

Find the standard representation of the following function

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

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

Find the representation of the product of the following function

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

$(x-3)(x-4)$

Find the representation of the product of the following function

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

$(x-3)(x+1)$

Find the representation of the product of the following function

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

$(x-6)(x+3)$