Standard Representation: Transition between different representations of a function

Find the standard representation of the following function

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

We will use the expanded distributive property.

(a+1)⋆(b+2) = ab+2a+b+2

Let's substitute the given values and solve:

(x-2)(x+5) =

x²-2x+5x+-2*5=

x²+3x-10

And that's the solution!

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

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

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

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

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

$f(x)=x^2-5x+9$

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

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

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

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

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

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

Find the standard representation of the following function

$f(x)=(x-5)^2-10$

$f(x)=x^2-10x+15$

Find the standard representation of the following function

$f(x)=(x+5)^2+3$

$f(x)=x^2+10x+28$

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

$f(x)=(-x+1)^2+3$

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

Find the standard representation of the following function

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

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

Find the standard representation of the following function

$f(x)=(x+4)^2-16$

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

Find the standard representation of the following function

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

$f(x)=x^2-4x+7$

Find the representation of the product of the following function

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

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

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

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

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

Find the representation of the product of the following function

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

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

Find the standard representation of the following function

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

$f(x)=x^2-10x+36$