For Exercises 59–64, use the standard form of a parabola given by y = a x 2 + b x + c to write an equation of a parabola that passes through the given points. (See Example 5.) ( 0 , 3 ) , ( 3 , 0 ) , ( − 1 , 8 )
For Exercises 59–64, use the standard form of a parabola given by y = a x 2 + b x + c to write an equation of a parabola that passes through the given points. (See Example 5.) ( 0 , 3 ) , ( 3 , 0 ) , ( − 1 , 8 )
Solution Summary: The equation of the parabola passes through the given points (0,3),
For Exercises 59–64, use the standard form of a parabola given by
y
=
a
x
2
+
b
x
+
c
to write an equation of a parabola that passes through the given points. (See Example 5.)
In Exercises 5–12, find the standard form of the equation of each
hyperbola satisfying the given conditions.
5. Foci: (0, –3), (0, 3); vertices: (0, –1), (0, 1)
6. Foci: (0, –6), (0, 6); vertices: (0, -2), (0, 2)
7. Foci: (-4, 0), (4, 0); vertices: (-3, 0), (3,0)
8. Foci: (-7, 0), (7, 0); vertices: (-5, 0), (5,0)
9. Endpoints of transverse axis: (0, -6), (0, 6); asymptote:
y = 2x
10. Endpoints of transverse axis: (-4,0), (4, 0); asymptote:
y = 2r
11. Center: (4, -2); Focus: (7, -2); vertex: (6, -2)
12. Center: (-2, 1); Focus: (-2, 6); vertex: (-2, 4)
Exercises 98–100 will help you prepare for the material covered
in the first section of the next chapter.
98. a. Does (-5, –6) satisfy 2x – y = -4?
b. Does (-5, -6) satisfy 3x – 5y = 15?
99. Graph y = -x – 1 and 4x – 3y = 24 in the same
rectangular coordinate system. At what point do the graphs
intersect?
100. Solve: 7x – 2(-2x + 4) = 3.
In Exercises 85–88, find the vertex for each parabola. Then
determine a reasonable viewing rectangle on your graphing
utility and use it to graph the quadratic function.
85. y = -0.25x² + 40x
86. y = -4x? + 20x + 160
87. y = 5x² + 40x + 600
88. y = 0.01x² + 0.6x + 100
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