Solved: In 6976, (a) find the intercepts of each equation,

Solve: 21x + 32 - 1 = - 7 (pp. A43A44) 2

Solve: x2 - 4x - 12 = 0 (pp. A46A47)

The points, if any, at which a graph crosses or touches the coordinate axes are called ___________.

The x-intercepts of the graph of an equation are those x-values for which ___________.

If for every point (x, y) on the graph of an equation the point (-x, y) is also on the graph, then the graph is symmetric with respect to the ___________.

If the graph of an equation is symmetric with respect to the y-axis and -4 is an x-intercept of this graph, then ________ is also an x-intercept.

If the graph of an equation is symmetric with respect to the origin and (3, -4) is a point on the graph, then ________ is also a point on the graph.

True or False To find the y-intercepts of the graph of an equation, let x = 0 and solve for y.

True or False The y-coordinate of a point at which the graph crosses or touches the x-axis is an x-intercept.

True or False If a graph is symmetric with respect to the x-axis, then it cannot be symmetric with respect to the y-axis.

In Problems 1122, find the intercepts and graph each equation by plotting points. Be sure to label the intercepts.y = x + 2 1

In Problems 1122, find the intercepts and graph each equation by plotting points. Be sure to label the intercepts.y = x - 6 1

In Problems 1122, find the intercepts and graph each equation by plotting points. Be sure to label the intercepts.y = 2x + 8 1

In Problems 1122, find the intercepts and graph each equation by plotting points. Be sure to label the intercepts.y = 3x - 9

In Problems 1122, find the intercepts and graph each equation by plotting points. Be sure to label the intercepts.y = x2 - 1 1

In Problems 1122, find the intercepts and graph each equation by plotting points. Be sure to label the intercepts.y = x2 - 9

In Problems 1122, find the intercepts and graph each equation by plotting points. Be sure to label the intercepts.y = -x2 + 4

In Problems 1122, find the intercepts and graph each equation by plotting points. Be sure to label the intercepts.y = -x2 + 1

In Problems 1122, find the intercepts and graph each equation by plotting points. Be sure to label the intercepts.2x + 3y = 6 2

In Problems 1122, find the intercepts and graph each equation by plotting points. Be sure to label the intercepts.5x + 2y = 10 2

In Problems 1122, find the intercepts and graph each equation by plotting points. Be sure to label the intercepts.9x2 + 4y = 36 2

In Problems 1122, find the intercepts and graph each equation by plotting points. Be sure to label the intercepts.4x2 + y = 4

In Problems 2332, plot each point. Then plot the point that is symmetric to it with respect to (a) the x-axis; (b) the y-axis; (c) the origin.(3, 4) 2

In Problems 2332, plot each point. Then plot the point that is symmetric to it with respect to (a) the x-axis; (b) the y-axis; (c) the origin.(5, 3) 2

In Problems 2332, plot each point. Then plot the point that is symmetric to it with respect to (a) the x-axis; (b) the y-axis; (c) the origin.(-2, 1) 2

In Problems 2332, plot each point. Then plot the point that is symmetric to it with respect to (a) the x-axis; (b) the y-axis; (c) the origin.(4, -2) 2

In Problems 2332, plot each point. Then plot the point that is symmetric to it with respect to (a) the x-axis; (b) the y-axis; (c) the origin.(5, -2)

In Problems 2332, plot each point. Then plot the point that is symmetric to it with respect to (a) the x-axis; (b) the y-axis; (c) the origin.(-1, -1) 2

In Problems 2332, plot each point. Then plot the point that is symmetric to it with respect to (a) the x-axis; (b) the y-axis; (c) the origin. (-3, -4) 3

In Problems 2332, plot each point. Then plot the point that is symmetric to it with respect to (a) the x-axis; (b) the y-axis; (c) the origin.(4, 0) 3

In Problems 2332, plot each point. Then plot the point that is symmetric to it with respect to (a) the x-axis; (b) the y-axis; (c) the origin.(0, -3) 3

In Problems 2332, plot each point. Then plot the point that is symmetric to it with respect to (a) the x-axis; (b) the y-axis; (c) the origin. (-3, 0)

In Problems 3340, the graph of an equation is given. (a) Find the intercepts. (b) Indicate whether the graph is symmetric with respect to the x-axis, the y-axis, or the origin.

In Problems 3340, the graph of an equation is given. (a) Find the intercepts. (b) Indicate whether the graph is symmetric with respect to the x-axis, the y-axis, or the origin.

In Problems 3340, the graph of an equation is given. (a) Find the intercepts. (b) Indicate whether the graph is symmetric with respect to the x-axis, the y-axis, or the origin.

In Problems 3340, the graph of an equation is given. (a) Find the intercepts. (b) Indicate whether the graph is symmetric with respect to the x-axis, the y-axis, or the origin.

In Problems 3340, the graph of an equation is given. (a) Find the intercepts. (b) Indicate whether the graph is symmetric with respect to the x-axis, the y-axis, or the origin.

In Problems 3340, the graph of an equation is given. (a) Find the intercepts. (b) Indicate whether the graph is symmetric with respect to the x-axis, the y-axis, or the origin.

In Problems 3340, the graph of an equation is given. (a) Find the intercepts. (b) Indicate whether the graph is symmetric with respect to the x-axis, the y-axis, or the origin.

In Problems 3340, the graph of an equation is given. (a) Find the intercepts. (b) Indicate whether the graph is symmetric with respect to the x-axis, the y-axis, or the origin.

In Problems 4144, draw a complete graph so that it has the type of symmetry indicated.

In Problems 4144, draw a complete graph so that it has the type of symmetry indicated.

In Problems 4144, draw a complete graph so that it has the type of symmetry indicated.

In Problems 4144, draw a complete graph so that it has the type of symmetry indicated.

In Problems 4560, list the intercepts and test for symmetry.y2 = x + 4 4

In Problems 4560, list the intercepts and test for symmetry.y2 = x + 9

In Problems 4560, list the intercepts and test for symmetry.y = 13 x 4

In Problems 4560, list the intercepts and test for symmetry.y = 1 5 x

In Problems 4560, list the intercepts and test for symmetry.y = x4 - 8x2 - 9

In Problems 4560, list the intercepts and test for symmetry.y = x4 - 2x2 - 8

In Problems 4560, list the intercepts and test for symmetry.9x2 + 4y2 = 36 5

In Problems 4560, list the intercepts and test for symmetry.4x2 + y2 = 4

In Problems 4560, list the intercepts and test for symmetry.y = x3 - 27

In Problems 4560, list the intercepts and test for symmetry.y = x4 - 1 5

In Problems 4560, list the intercepts and test for symmetry.y = x2 - 3x - 4

In Problems 4560, list the intercepts and test for symmetry.y = x2 + 4

In Problems 4560, list the intercepts and test for symmetry.y = 3xx2 + 9

In Problems 4560, list the intercepts and test for symmetry.y = x2 - 4

In Problems 4560, list the intercepts and test for symmetry.y = -x3

In Problems 4560, list the intercepts and test for symmetry.y = x4 + 1

In Problems 6164, draw a quick sketch of each equation.y = x3

In Problems 6164, draw a quick sketch of each equation.

In Problems 6164, draw a quick sketch of each equation.

In Problems 6164, draw a quick sketch of each equation.

If (3, b) is a point on the graph of y = 4x + 1, what is b? 6

If (-2, b) is a point on the graph of 2x + 3y = 2, what is b?

If (a, 4) is a point on the graph of y = x2 + 3x, what is a? 6

If (a, -5) is a point on the graph of y = x2 + 6x, what is a?

In Problems 6976, (a) find the intercepts of each equation, (b) test each equation for symmetry with respect to the x-axis, the y-axis, and the origin, and (c) graph each equation by hand by plotting points. Be sure to label the intercepts on the graph and use any symmetry to assist in drawing the graph. Verify your results using a graphing utility.y = x2 - 5

In Problems 6976, (a) find the intercepts of each equation, (b) test each equation for symmetry with respect to the x-axis, the y-axis, and the origin, and (c) graph each equation by hand by plotting points. Be sure to label the intercepts on the graph and use any symmetry to assist in drawing the graph. Verify your results using a graphing utility.y = x2 - 8

In Problems 6976, (a) find the intercepts of each equation, (b) test each equation for symmetry with respect to the x-axis, the y-axis, and the origin, and (c) graph each equation by hand by plotting points. Be sure to label the intercepts on the graph and use any symmetry to assist in drawing the graph. Verify your results using a graphing utility.x - y2 = -9

In Problems 6976, (a) find the intercepts of each equation, (b) test each equation for symmetry with respect to the x-axis, the y-axis, and the origin, and (c) graph each equation by hand by plotting points. Be sure to label the intercepts on the graph and use any symmetry to assist in drawing the graph. Verify your results using a graphing utility.x + y2 = 4

In Problems 6976, (a) find the intercepts of each equation, (b) test each equation for symmetry with respect to the x-axis, the y-axis, and the origin, and (c) graph each equation by hand by plotting points. Be sure to label the intercepts on the graph and use any symmetry to assist in drawing the graph. Verify your results using a graphing utility.x2 + y2 = 9

In Problems 6976, (a) find the intercepts of each equation, (b) test each equation for symmetry with respect to the x-axis, the y-axis, and the origin, and (c) graph each equation by hand by plotting points. Be sure to label the intercepts on the graph and use any symmetry to assist in drawing the graph. Verify your results using a graphing utility.x2 + y2 = 16

In Problems 6976, (a) find the intercepts of each equation, (b) test each equation for symmetry with respect to the x-axis, the y-axis, and the origin, and (c) graph each equation by hand by plotting points. Be sure to label the intercepts on the graph and use any symmetry to assist in drawing the graph. Verify your results using a graphing utility.y = x3 - 4x

In Problems 6976, (a) find the intercepts of each equation, (b) test each equation for symmetry with respect to the x-axis, the y-axis, and the origin, and (c) graph each equation by hand by plotting points. Be sure to label the intercepts on the graph and use any symmetry to assist in drawing the graph. Verify your results using a graphing utility.y = x3 - x

Given that the point (1, 2) is on the graph of an equation that is symmetric with respect to the origin, what other point is on the graph?

If the graph of an equation is symmetric with respect to the y-axis and 6 is an x-intercept of this graph, name another x-intercept.

If the graph of an equation is symmetric with respect to the origin and -4 is an x-intercept of this graph, name another x-intercept.

If the graph of an equation is symmetric with respect to the x-axis and 2 is a y-intercept, name another y-intercept.

In studios and on stages, cardioid microphones are often preferred for the richness they add to voices and for their ability to reduce the level of sound from the sides and rear of the microphone. Suppose one such cardioid pattern is given by the equation (x2 + y2 - x) 2 = x2 + y2 . (a) Find the intercepts of the graph of the equation. (b) Test for symmetry with respect to the x-axis, y-axis, and origin.

The solar electric generating systems at Kramer Junction, California, use parabolic troughs to heat a heat-transfer fluid to a high temperature. This fluid is used to generate steam that drives a power conversion system to produce electricity. For troughs 7.5 feet wide, an equation for the cross-section is 16y2 = 120x - 225.

Draw a graph of an equation that contains two x-intercepts; at one the graph crosses the x-axis, and at the other the graph touches the x-axis.

Make up an equation with the intercepts (2, 0), (4, 0), and (0, 1). Compare your equation with a friends equation. Comment on any similarities.

Draw a graph that contains the points (0, 1), (1, 3), and (3, 5) and is symmetric with respect to the x-axis. Compare your graph with those of other students. Are most of the graphs almost straight lines? How many are curved? Discuss the various ways that these points might be connected.

An equation is being tested for symmetry with respect to the x-axis, the y-axis, and the origin. Explain why, if two of these symmetries are present, the remaining one must also be present.

Draw a graph that contains the points (-2, 5), (-1, 3), and (0, 2) that is symmetric with respect to the y-axis. Compare your graph with those of other students; comment on any similarities. Can a graph contain these points and be symmetric with respect to the x-axis? The origin? Why or why not

Open the y-axis symmetry applet. Move point A around the Cartesian plane with your mouse. How are the coordinates of point A and the coordinates of point B related?

Open the x-axis symmetry applet. Move point A around the Cartesian plane with your mouse. How

Open the origin symmetry applet. Move point A around the Cartesian plane with your mouse. How are the coordinates of point A and the coordinates of point B related?