IM Alg2.3.6 Lesson: Squares and Square Roots
Find the solutions of each equation mentally.
Clare was adding and , and at first she wrote . But then she remembered that 2 and -2 both square to make 4, and that 3 and -3 both square to make 9. She wrote down all the possible combinations: 2 + 3 = 5 2 + (-3) = -1 (-2) + 3 = 1 (-2) + (-3) = -5 Then she wondered, “Which of these are the same as ? All of them? Or only some? Or just one?” How would you answer Clare’s question? Give reasons that support your answer.
How many solutions are there to each equation?
Write a rule to determine how many solutions there are to the equation where and are non-zero integers.
Complete the table with the exact values and label the corresponding points on the graph with the exact values.
Label the point on the graph above that shows the solution to .
Label the point on the graph above that shows the solution to .
Label the point on the graph above that shows the solution to .
The graph of is shown t=s².
Label the point(s) on the graph that show(s) the solution(s) to .
Label the point(s) on the graph that show(s) the solution(s) to .
Label the point(s) on the graph that show(s) the solution(s) to .