Two students are working to sketch the graph of the function

Two students are working to sketch the graph of the function k(x) = 1.5(x - 2)^2 + 4. Both girls begin by imagining a horizontal translation of the graph of y = x^2. However they proceed differently and notice they get different results. Their work is shown below. To help the girls understand who is correct, define the function rules for each graph the girls drew. a. f(x) = b. g(x) = c. h(x) = d. s(x) = e. r(x) = f. p(x) =

Solution

y=x²

a)f(x)=(x-2)²

b)g(x)=(x-2)²+4

c)h(x)=1.5((x-2)²+4)=1.5(x-2)²+6

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d)s(x)=(x-2)²

e)r(x)=1.5(x-2)²

f)p(x)=1.5(x-2)² +4

susie is correct

transformations:

step 1: translate graph to right by 2 units

step2:vertically stretch graph by 1.5 times

step3: translate graph upwards by 4 units