Lesson 7.6 Square, Squaring, and Parabolas To learn about the squaring and square root functions To graph parabolas To compare the squaring function with other functions To related the squaring function to finding the area of a square Lesson 7.6

Think of a number between 1 and 10. Multiply it by itself Think of a number between 1 and 10. Multiply it by itself. What number did you get? Try it again with the opposite of your number. Did you get the same result? The result is called a square of a number. The process of multiplying a number by itself is called squaring a number.

The square of a number x is x2. Try entering -32 and (-3)2 on your calculator. Which result is the square of -3? Many real-world situations, such as calculating the area of squares and circles, involve squaring. Do you think the rule for squaring is a function? In order to answer this question you will graph the relationship between numbers and their squares.

Graphing a Parabola Make a table with column headings like the ones shown. Put the numbers - 10 through 10 in the first column and then enter these numbers in L1 on your calculator. Without the calculator, find the square of each number and place it in the second column. Check your results by squaring L1 with the x2 key. Store these numbers in L2.

Graphing a Parabola How do the squares of the numbers and their opposites compare? What is the relationship between the positive numbers and their squares? Between the negative numbers and their squares?

Graphing a Parabola Choose an appropriate window and plot points in the form (L1, L2). Graph y1=x2 on the same set of axes. What relationship does this graph show? Is the graph of y1=x2 the graph of a function? If so, describe the domain and range. If not, explain why not.

The graph of y=x2 is called a parabola. The points of the parabola for y=x2 are in what quadrants? What makes the point (0,0) on your curve unique? Where is this point on the parabola? Draw a vertical line through the point (0,0). How is this line like a mirror?

Compare your parabola with the graph of the absolute value function, y = |x|. How are they alike and how are they different?

Which x- and y-values in your parabola could represent side lengths and areas of squares?

Example Find the side of the square whose area is 6.25 square centimeters. Use a graph to check your answer. 6.25 sq. cm.