Rev Name Date. Solve each of the following equations for y by isolating the square and using the square root property.

Transcription

1 Rev Name Date TI-8 GC 3 Using GC to Graph Parabolae that are Not Functions of Objectives: Recall the square root propert Practice solving a quadratic equation f Graph the two parts of a hizontal parabola Identif the ais of smmetr and its equation When solving f a variable epression that has been squared, recall that there are usuall two solutions. Eample: 9 can be facted to ( 3)( 3) 0, giving solutions 3, 3. The square root propert tells us to use ± when we take the square root of both sides of 9. Solve each of the following equations f b isolating the square and using the square root propert. ) ) ( ) ) ( ) 3) ( ) ) ( ) When we graph using the GC, we have onl the Y menu, not an X menu. So we must have as a function of, not an epression in, an epression in. Solve f first, using algebra. If the square root propert was used, write each of the two functions. 6) Graph on the GC. Step : Solve the equation f using the square root propert; ± gives ±. Step : Write as two functions. and Step 3: Enter these two functions into the GC Y menu and graph. Copright 0 b Martha Fidler Care. Permission to reproduce is given onl to current Southwestern College instructs and students.

2 Rev TI-8 GC 3 Using GC to Graph Parabolae that are Not Functions of Page The verte of a hizontal parabola can be found from the standard fm of the equation, just as it was f a quadratic function. The roles of and are reversed. a( k) h is the standard fm of the equation, and (h,k) is the verte. The ais of smmetr is a hizontal line through the verte, with equation k. Notice that the -coefficient of the verte, k, is inside the parentheses, net to the variable. If a>0, the parabola opens in the positive -direction, to the right. If a<0, the parabola opens in the negative -direction, to the left. 7) Find the verte of ( ) Does this parabola open left right? 8) Find the equation of the ais of smmetr. 9) Solve ( ) f its two functions. Make a table on the GC f the two functions. Step : Solve the equation f using the square root propert; (Use our previous wk.) Step : Write as two functions. Step 3: Enter these two functions into the GC Y menu and graph. Step : Set up the GC table to begin at the verte. If the parabola opens left, ou ll use the If the parabola opens right, use ke to move through the table. to move through the table. Use the GC table to fill in this chart: -value 0 9 0) Notice that the -values provided to ou in the previous chart have a pattern. What is it? Copright 0 b Martha Fidler Care. Permission to reproduce is given onl to current Southwestern College instructs and students.

3 Rev TI-8 GC 3 Using GC to Graph Parabolae that are Not Functions of Page 3 ) Find the verte of ( ) Does this parabola open left right? ) Find the equation of the ais of smmetr of ( ) 3) Solve ( ). f its two functions. Make a table on the GC f the two functions. Step : Solve the equation f using the square root propert; (Use our previous wk.) Step : Write as two functions. Step 3: Enter these two functions into the GC Y menu and graph. Step : Set up the GC table to begin at the verte. Use the GC table to fill in this chart: -value 0 0 ) Draw aes and label them with an appropriate scale. Plot the points and graph both of the curves, to get the hizontal parabola. Sketch the ais of smmetr. Copright 0 b Martha Fidler Care. Permission to reproduce is given onl to current Southwestern College instructs and students.

4 Rev TI-8 GC 3 Using GC to Graph Parabolae that are Not Functions of, page Graph. You ma wish to use these steps: a. Does this parabola open left right? b. What is the verte? c. What is the equation of the ais of smmetr? d. Solve f, write two functions. e. Make a table. f. Draw aes and label them with an appropriate scale. Plot the points and graph parabola. Sketch the ais of smmetr. ) Graph ( ) Shtcut: The dered pairs (,) that satisf ( ) Copright 0 b Martha Fidler Care. Permission to reproduce is given onl to current Southwestern College instructs and students. can be changed (swap f and f ) to get dered pairs that satisf ( ). Because ( ) is alread a function of, no solving f is needed. To use this shtcut, skip step d. above, and make a table of values f ( ). Then make a second table f graphing ( ) b swapping f and f. If this shtcut doesn t make sense to ou, don t use it.

5 Rev TI-8 GC 3 Using GC to Graph Parabolae that are Not Functions of, page Graph. You ma wish to use these steps: a. Does this parabola open left right? b. What is the verte? c. What is the equation of the ais of smmetr? d. Solve f, write two functions. (Or use the shtcut) e. Make a table. f. Draw aes and label them with an appropriate scale. Plot the points and graph parabola. Sketch the ais of smmetr. 6) Graph ( ) Copright 0 b Martha Fidler Care. Permission to reproduce is given onl to current Southwestern College instructs and students.

6 Rev TI-8 GC 3 Using GC to Graph Parabolae that are Not Functions of, solutions, page 6 ) ± ) ± 3) ) ) ± ± ± ± ± ( ) ± ± ( ) 6) 7) V(0,) a>0, opens right. 8) 9) ±, cont -value ) The -values are all perfect squares. ) V(0,) ) 3) ± ± ;, Copright 0 b Martha Fidler Care. Permission to reproduce is given onl to current Southwestern College instructs and students.

7 Rev Copright 0 b Martha Fidler Care. Permission to reproduce is given onl to current Southwestern College instructs and students. TI-8 GC 3 Using GC to Graph Parabolae that are Not Functions of, solutions, page 7 ) ) opens right, V(-,), ais, ±, -value ) opens left, V(-,), ais, ±, -value