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 axis.
The factored form of the quadratic function looks like this:
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 axis.
The factored form of the quadratic function looks like this:
Find the standard representation of the following function
\( f(x)=(x-2)(x+5) \)
Where
and are the intersection points of the parabola with the axis.
In the following way:
Let's see an example of the factored form:
We can determine that:
the intersection points with the axis are:
Notice that, since there is a minus sign in the original form before and , we can deduce that if there is a plus sign before one of them it is negative and, therefore and not .
Determine the points of intersection of the function
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!
Find the standard representation of the following function
\( f(x)=(x-6)(x-2) \)
Find the standard representation of the following function
\( f(x)=(x+2)(x-4) \)
Find the standard representation of the following function
\( f(x)=3x(x+4) \)