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.
+486 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.
