Note that the number within the parentheses must be positive, as no number can be found which multiplied by itself gives a negative number. For this reason y cannot be greater than 5. Why? In computing the values of x make use of the square-root tables on page 232.

EXERCISES

1. Check the graph for equation (1), page 170.

2. Check the above graph.

3. Supply the values of x that are lacking in the table above and compute the corresponding values of y.

4. From the graph on page 170 find the value of y when

x is 3; 2; 3.5; 1.25; -2.25; 0.5; - 0.25.

5. From the above graph find the value of y when x is 2.5; 1.5; 0.5; 2.75; -3.25; 0.75.

12. The space in feet, s, that a body falls from rest in any number of seconds, t, is expressed by the equation,

s = 16t2.

In graphing the above equation place t along the horizontal axis, letting 4 spaces represent 1 sec. If you have 26 vertical spaces, let each one represent 10 ft.; otherwise use some other arrangement, so that 260 ft. can be represented for the space s.

13. Read from the graph the distance which a body will fall in the first 1.5 sec.; first 2.5 sec.; first 3.5 sec.

14. Read from the graph how long it will take a body to fall 16 ft.; 64 ft.; 50 ft.; 150 ft.; 200 ft.

15. Read from the graph how far a body falls in the 2d second; in the 3d second; in the 4th second.

16. A body dropped from rest will continually gain velocity. If it is dropped from a height, h, its velocity will be expressed by the equation,

Graph this equation and check.

17. Read from the graph what velocity a body will attain if dropped from a height of 25 ft.; 100 ft.; 36 ft.; 62.5 ft. Read from the graph from what height a body must be dropped to gain a velocity of 16 ft. per second; of 20 ft. per second; of 32 ft. per second; of 40 ft. per second.

18.

19. Graph one of the geometrical formulas found on page 226 that contains only two variables. Use the table of square roots when helpful in finding the corresponding values of the variables. Check the work. Explain how to read the graph.

160. Simultaneous Quadratics.-First recall the meaning of simultaneous equations or reread pages 136 and 137. The horizontal distance gives the length of the radius for both graphs. For C the vertical axis gives the length of the circumference of the circle as in linear feet or linear meters. For A the vertical axis gives the area of the circle as in square feet or square meters. The two graphs cut each other in two points, (0, 0) and (2, 124), as is seen in the figure. These values which satisfy the two operations are the simultaneous solutions of the two equations.

EXERCISES

1. Find the values of C and A when R is .5 ft.; 1.5 in.; 2 cm.; 1.5 dm.; 1 in.; 1.25 m.

2. Find the value of A when C is 5 in.; 8.5 ft.; 12 cm.

3. Find the value of C when A is 4 sq. in.; 6 sq. ft.; 8 cm.2; 12.5 m.2; 8.25 sq. ft.

Equation (1) above is graphed just as the equation on page 171. In order to graph (2) it is first solved for x when

Negative as well as positive values are assigned to y to find the corresponding value of x. Care must always be taken not to omit parts of a graph, as would have been done here if negative values had not been assigned to y. Note that O cannot be used as one value for y, because 2 has no meaning. A peculiar part of the graph of (2) is that it has two distinct branches.

The two graphs intersect in four points. The equations have, therefore, four simultaneous solutions. What are they? Check each set by substituting in both equations.

EXERCISES

Graph the following sets of simultaneous equations and

check the graph of each equation. Pick out the simultaneous solutions and check by substitution in the equations:

13. The sum of two numbers is 5. Represent this by an equation and graph it. The product of the two numbers is 4. State this by an equation and graph it. Pick out the simultaneous solutions and check.

f

14. The equations giving the distance a body falls from rest and the velocity it attains are f = 16t2 and ƒ = 32t. Graph both to the same set of axes, using t for the horizontal axis. What are the points of intersection? What do they tell? Check in the equations.

15. Express by an equation that the length of a rectangle is 2 ft. more than the width. Express by an equation that the area of the rectangle is 48 sq. ft. Graph each equation and find the values of length and of width satisfying both equations; that is, solve the two equations.

Hold a number contest, using whole numbers and decimals.