Factored form of the quadratic function

🏆Practice representation as a product

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)

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Find the standard representation of the following function

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

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tt and kk are the intersection points of the parabola with the XX axis.
In the following way: (t,0)(k,0)(t,0) (k,0)
Let's see an example of the factored form:

y=(x7)×(x+2)y=(x-7) \times (x+2)
We can determine that:

the intersection points with the XX axis are:
(7,0) (7,0) 
 (2,0) (- 2,0)
Notice that, since there is a minus sign in the original form before kk and tt, we can deduce that if there is a plus sign before one of them it is negative and, therefore 2-2 and not 22.

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