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Adrian Romanelli · Answer 1 · 2023-12-22T23:41:44+0000

Step-by-step explanation:

We were given the equation:

$f\mleft(x\mright)=(x-2)^2-4$

We will proceed to expand the equation as shown below:

$\begin{gathered} f\mleft(x\mright)=(x-2)^2-4 \\ f(x)=x(x-2)-2(x-2)-4 \\ f(x)=x^2-2x-2x+4-4 \\ f(x)=x^2-4x \end{gathered}$

We will proceed to graph the equation derived above as shown below:

$\begin{gathered} f(x)=x^(2)-4x \\ \\ when:x=-4 \\ f(x)=(-4)^2-4(-4)=16+16=32 \\ (x,y)=(-4,32) \\ \\ when:x=-3 \\ f(x)=(-3)^2-4(-3)=9+12=21 \\ (x,y)=(-3,21) \\ \\ when:x=-2 \\ f(x)=(-2)^2-4(-2)=4+8=12 \\ (x,y)=(-2,12) \\ \\ when:x=-1 \\ f(x)=(-1)^2-4(-1)=1+4=5 \\ (x,y)=(-1,5) \\ \\ when:x=0 \\ f(x)=0^2-4(0)=0 \\ (x,y)=(0,0) \\ \\ when:x=1 \\ f(x)=1^2-4(1)=1-4=-3 \\ (x,y)=(1,-3) \\ \\ when:x=2 \\ f(x)=2^2-4(2)=4-8=-4 \\ (x,y)=(2,-4) \\ \\ when:x=3 \\ f(x)=3^2-4(3)=9-12=-3 \\ (x,y)=(3,-3) \\ \\ when:x=4 \\ f(x)=4^2-4(4)=16-16=0 \\ (x,y)=(4,0) \\ \\ when:x=8 \\ f(x)=8^2-4(8)=64-32=32 \\ (x,y)=(8,32) \end{gathered}$

We will plot this on a graph, we have:

Graph the equation f(x) = (x-2)^2 - 4-example-1

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