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Describe three different strategies you could use to verify that these equations are identical:

1) quadratic function:  y=0.6(x+4)2+2.4

 2) vertex form of the function: y=0.6x2+4.8x+12.

 

Choose one of the strategies you described and demonstrate whether or not the two functions are equivalent.

 Apr 6, 2021
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You could either a) expand equation 1, b) complete the square on equation 2, c) set up equation 1 equals equation 2 and cancel/simplify

 

I'll choose completing the square, because expanding is pretty self explanatory.

 

Completing the square on equation two:

 

First, factor an 0.6 out of the first two terms, yielding $0.6(x^2+8x)+12$

 

Second, complete the square on the first two terms by adding a constant, yielding $0.6(x^2+8x+16)-0.6*16+12$.

 

Simplifying gives $0.6(x+4)^2-0.6*16+12$.

 

Simplifying further gives $0.6(x+4)^2+2.4$.

 

Now, setting them equal, we have $0.6(x+4)^2+2.4=0.6(x+4)^2+2.4$, which is true. So, these two functions are equivalent.

 Apr 6, 2021

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