B Apply

Sketch each parabola using the given information.

33. vertex (3, 6), y-intercept 2
34. vertex ( − 1 , − 4 ) , open negative 1 comma negative 4 close comma  y-intercept 3
35. vertex (0, 5), point ( 1 , − 2 ) open 1 comma negative 2 close
36. vertex (2, 3), point (6, 9)
37. Think About a Plan Suppose you work for a packaging company and are designing a box that has a rectangular bottom with a perimeter of 36 cm. The box must be 4 cm high. What dimensions give the maximum volume?
    • How can you model the volume of the box with a quadratic function?
    • What information can you get from the function to find the maximum volume?
38. Landscaping A town is planning a playground. It wants to fence in a rectangular space using an existing wall. What is the greatest area it can fence in using 100 ft of donated fencing?

    

For each function, the vertex of the function's graph is given. Find the unknown coefficients.

39. y = x 2 + b x + c ; ( 3 , − 4 ) y equals , x squared , plus b x plus c semicolon open 3 comma negative 4 close
40. y = − 3 x 2 + b x + c ; y equals negative 3 , x squared , plus b x plus c semicolon  (1, 0)
41. y = a x 2 + 10 x + c ; ( − 5 , − 27 ) y equals eh , x squared , plus 10 x plus c semicolon open negative 5 comma negative 27 close
42. y = c − a x 2 − 2 x ; ( − 1 , 3 ) y equals c minus eh , x squared , minus 2 x semicolon open negative 1 comma 3 close
43. Physics The equation for the motion of a projectile fired straight up at an initial velocity of 64 ft/s is h = 64 t − 16 t 2 , h equals 64 , t minus , 16 , t squared , comma  where h is height in feet and t is time in seconds. Find the time the projectile needs to reach its highest point. How high will it go?
44. A student says that the graph of y = a x 2 + b x + c y equals eh , x squared , plus b x plus c  gets wider as a increases.
    1. Error Analysis Use examples to show that the student is wrong.
    2. Writing Summarize the relationship between | a | absolute value of eh ,  and the width of the graph of y = a x 2 + b x + c . y equals eh , x squared , plus b x plus c .

For each function, find the y-intercept.

45. y = ( x − 1 ) 2 + 2 y equals open x minus 1 , close squared , plus 2
46. y = − 3 ( x + 2 ) 2 − 4 y equals negative 3 open x plus 2 , close squared , minus 4
47. y = − 2 3 ( x − 9 ) 2 y equals negative , 2 thirds , open x minus 9 , close squared

C Challenge

For each function, the vertex of the function's graph is given. Find a and b.

48. y = a x 2 + b x − 27 ; ( 2 , − 3 ) y equals eh , x squared , plus b x minus 27 semicolon open 2 comma negative 3 close
49. y = a x 2 + b x + 5 ; ( − 1 , 4 ) y equals eh , x squared , plus b x plus 5 semicolon open negative 1 comma 4 close
50. y = a x 2 + b x + 8 ; ( 2 , − 4 ) y equals eh , x squared , plus b x plus 8 semicolon open 2 comma negative 4 close
51. y = a x 2 + b x ; ( − 3 , 2 ) y equals eh , x squared , plus b x semicolon open negative 3 comma 2 close

Sketch each parabola using the given information.

52. axis of symmetry x = 1, y-intercept 3, point ( − 1 , 6 ) open negative 1 comma 6 close
53. axis of symmetry x = 2, y-intercept 1, point (3, 2.5)

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