Question 1

a) Plot a graph of the function (((x-3))^2)-7.

b) Write down what you think the two roots are.

c) Use FindRoot to find both roots of the equation (((x-3))^2)-7.

Question 2

A student is part way through trying to find the roots for (((x-2))^2)-2. They have plotted the graph below.

Plot[(((x-2))^2)-2,{x,0,5}]

Additionally they have written the following list of values.

list={0,4}(*remember to evaluate this code*)

a) They are part way through defining a function that will find the root of an equation if you input a guess. Help the student to correct the 1 syntax error they made in the code below.

f[x_]:=(((x-2))^2)-2 (*remember to evaluate this code*)

FindFunction[guess_]:=FindRoot[f[x],x,guess]

b) Now use either Method 1 or Method 2 to find the two roots of the equation.