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Analyzing Two Sets of Equations

7.15.1 Analyzing Two Sets of Equations

7.15.1 • Analyzing Two Sets of Equations

Warm Up

Set 1:

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

g ( x ) = x ( x + 4 ) g ( x ) = x ( x + 4 )

h ( x ) = ( x + 2 ) 2 − 4 h ( x ) = ( x + 2 ) 2 − 4

Set 2:

p ( x ) = − x 2 + 6 x − 5 p ( x ) = − x 2 + 6 x − 5

q ( x ) = ( 5 − x ) ( x − 1 ) q ( x ) = ( 5 − x ) ( x − 1 )

r ( x ) = − 1 ( x − 3 ) 2 + 4 r ( x ) = − 1 ( x − 3 ) 2 + 4

1.

After observing the two sets, what do you notice?

Compare your answer:

Things you notice:

  • Each set has three equations.
  • Each equation has the output in function notation on the left side of the equal sign, and an expression on the right side.
  • The expressions are in standard form, factored form, and one other form.
  • The equations in standard and factored form are equivalent.
2.

After observing the two sets, what do you wonder?

Compare your answer:

Things you may wonder:

  • Why are the equations in each set grouped together?
  • In each set, is the expression in the last equation written in a particular form? What is it called?
  • In each set, is the expression in the last equation equivalent to the other two?