Chapter 10

Chapter 10

When finding solution(s) to a system of equations, 4, and 7, students can graph the system. Can estimate the solutions(s), if any, from the graph before solving the system algebraically to find an exact solution.

Students who have difficulty may not understand how to combine the equations. Pay attention that the equation they need to find will have t as the input and give the area as the output. To find this equation, substitute 2t - 1 for r in the first equation and simplify.

Type of function?

Type of function?

Students who find an incorrect answer for the second table may not have recognized that second differences for this table are constant. x is changing by a constant amount, and the second differences for y are also constant. Therefore, the data is quadratic.

For the graphs of two quadratic functions

how many points of intersection are possible?

How long after the jump will it take for Teo to

reach his maximum height?

0.25 seconds

At his maximum height, how far above the level of the diving board will Teo be?

1 Foot

How long will it take Teo to reach the water?

1 second

Students who give an answer of 9 feet for the second question, may have been finding the distance above the water. Remember that the question asks for the distance above the diving board. Since the diving board is 8 feet above the water, Teo is 1 foot above the diving board at his maximum height.

Students who did not find the correct vertex for the first function, may have had difficulty performing arithmetic operations on fractions. Review the steps, stressing the importance of writing each step to minimize the possibility of errors.

• A)Vertical stretch by a factor of 3, reflection across the x-axis, and translation 2 units up.

• What quadratic function models the shape of the mound? Include the meaning and units of the variables. y = -0.0327x2 + 0.5827x + 0.0462; x is the number of meters from the base of the mound; y is the depth of the mound in meters.

• Using the function you found, what do you estimate was the width of the mound?about 17.9 meters

• Using your function, what do you estimate was the depth of the mound at its deepest point?about 2.64 meters

Students who have difficulty defining variables may not have noticed that the measurements begin from the left side of the mound. Have students draw axes on the diagram to help identify the meaning of the variables.

Remember students to check answers for 11b and 11c for reasonableness. Since parabolas are symmetric and the mound is 1.5 meters deep at 3 meters and 1 meter deep at 16 meters, the

width must be less than 19 meters. This means that the vertex is at about 9 meters, so the deepest point is a bit deeper than the depth

at 11 meters, which is 2.5 meters.