Problem 1SP: 1. Given:
a. Write the function in the form .
b. Identify the vertex, axis of symmetry, and... Problem 2SP Problem 3SP: Given: f ( x ) = x 2 + 4 x + 6 a. Use the vertex formula to find the vertex of the parabola. b.... Problem 4SP: 4. An object is launched into the air with an initial velocity of ft/sec from the top of a building... Problem 5SP: Write an equation of the parabola that passes through the points ( 1 , 1 ) , ( − 2 , 1 ) , and ( 3... Problem 1PE: 1. a. Given (a ≠ 0), the vertex formula gives the x-coordinate of the vertex as ______________. The... Problem 2PE: How does the graph of f ( x ) = − 2 x 2 compare with the graph of y = x 2 ? Problem 3PE: How does the graph of p ( x ) = 1 4 x 2 compare with the graph of y = x 2 ? Problem 4PE: How does the graph of Q ( x ) = x 2 − 8 3 compare with the graph of y = x 2 ? Problem 5PE: How does the graph of r ( x ) = x 2 + 7 compare with the graph of y = x 2 ? Problem 6PE: How does the graph of s ( x ) = ( x − 4 ) 2 compare with the graph of y = x 2 ? Problem 7PE: How does the graph of t ( x ) = ( x + 10 ) 2 compare with the graph of y = x 2 ? Problem 8PE: Find the coordinates of the vertex of the parabola defined by g ( x ) = 2 ( x + 3 ) 2 − 4 . Problem 9PE: For Exercises 9–16, find the value of n to complete the square. Factor the resulting trinomial. x 2... Problem 10PE: For Exercises 9–16, find the value of n to complete the square. Factor the resulting... Problem 11PE: For Exercises 9–16, find the value of n to complete the square. Factor the resulting trinomial. y 2... Problem 12PE: For Exercises 9–16, find the value of n to complete the square. Factor the resulting... Problem 13PE: For Exercises 9–16, find the value of n to complete the square. Factor the resulting trinomial. b 2... Problem 14PE: For Exercises 9–16, find the value of n to complete the square. Factor the resulting trinomial. m 2... Problem 15PE: For Exercises 9–16, find the value of n to complete the square. Factor the resulting trinomial. t 2... Problem 16PE: For Exercises 9–16, find the value of n to complete the square. Factor the resulting trinomial. p 2... Problem 17PE: For Exercises 17–28, write the function in the form f ( x ) = a ( x − h ) 2 + k by completing the... Problem 18PE: For Exercises 17–28, write the function in the form f ( x ) = a ( x − h ) 2 + k by completing the... Problem 19PE: For Exercises 17–28, write the function in the form f ( x ) = a ( x − h ) 2 + k by completing the... Problem 20PE: For Exercises 17–28, write the function in the form by completing the square. Then identify the... Problem 21PE: For Exercises 17–28, write the function in the form by completing the square. Then identify the... Problem 22PE: For Exercises 17–28, write the function in the form f ( x ) = a ( x − h ) 2 + k by completing the... Problem 23PE: For Exercises 17–28, write the function in the form by completing the square. Then identify the... Problem 24PE: For Exercises 17–28, write the function in the form by completing the square. Then identify the... Problem 25PE: For Exercises 17–28, write the function in the form by completing the square. Then identify the... Problem 26PE: For Exercises 17–28, write the function in the form f ( x ) = a ( x − h ) 2 + k by completing the... Problem 27PE: For Exercises 17–28, write the function in the form f ( x ) = a ( x − h ) 2 + k by completing the... Problem 28PE: For Exercises 17–28, write the function in the form f ( x ) = a ( x − h ) 2 + k by completing the... Problem 29PE: For Exercises 29–40, find the vertex by using the vertex formula. (See Example 3.)
29.
Problem 30PE: For Exercises 29–40, find the vertex by using the vertex formula. (See Example 3.) T ( x ) = x 2 − 8... Problem 31PE: For Exercises 29–40, find the vertex by using the vertex formula. (See Example 3.) r ( x ) = − 3 x 2... Problem 32PE: For Exercises 29–40, find the vertex by using the vertex formula. (See Example 3.)
32.
Problem 33PE: For Exercises 29–40, find the vertex by using the vertex formula. (See Example 3.) N ( x ) = x 2 + 8... Problem 34PE: For Exercises 29–40, find the vertex by using the vertex formula. (See Example 3.) M ( x ) = x 2 + 6... Problem 35PE: For Exercises 29–40, find the vertex by using the vertex formula. (See Example 3.) m ( x ) = 1 2 x 2... Problem 36PE: For Exercises 29–40, find the vertex by using the vertex formula. (See Example 3.)
36.
Problem 37PE: For Exercises 29–40, find the vertex by using the vertex formula. (See Example 3.) k ( x ) = − x 2 +... Problem 38PE: For Exercises 29–40, find the vertex by using the vertex formula. (See Example 3.) h ( x ) = − x 2 +... Problem 39PE: For Exercises 29–40, find the vertex by using the vertex formula. (See Example 3.) A ( x ) = − 1 3 x... Problem 40PE: For Exercises 29–40, find the vertex by using the vertex formula. (See Example 3.)
40.
Problem 41PE: For Exercises 41–44, find the vertex two ways: a.by completing the square and writing in the form f... Problem 42PE: For Exercises 41–44, find the vertex two ways: a.by completing the square and writing in the form f... Problem 43PE: For Exercises 41–44, find the vertex two ways: a.by completing the square and writing in the form f... Problem 44PE: For Exercises 41–44, find the vertex two ways: a.by completing the square and writing in the form f... Problem 45PE: For Exercises 45–52
a. Find the vertex.
b. Find the y-intercept.
c. Find the x-intercept(s), if they... Problem 46PE: For Exercises 45–52
a. Find the vertex.
b. Find the y-intercept.
c. Find the x-intercept(s), if they... Problem 47PE: For Exercises 45–52 a.Find the vertex. b.Find the y-intercept. c. Find the x-intercept(s), if they... Problem 48PE: For Exercises 45–52 a.Find the vertex. b.Find the y-intercept. c. Find the x-intercept(s), if they... Problem 49PE: For Exercises 45–52
a. Find the vertex.
b. Find the y-intercept.
c. Find the x-intercept(s), if they... Problem 50PE: For Exercises 45–52 a.Find the vertex. b.Find the y-intercept. c. Find the x-intercept(s), if they... Problem 51PE: For Exercises 45–52 a.Find the vertex. b.Find the y-intercept. c. Find the x-intercept(s), if they... Problem 52PE: For Exercises 45–52 a.Find the vertex. b.Find the y-intercept. c. Find the x-intercept(s), if they... Problem 53PE: A set of fireworks mortar shells is launched from the staging platform at 100 ft/sec from an initial... Problem 54PE: 54. A baseball player throws a ball, and the height of the ball (in feet) can be approximated... Problem 55PE: Gas mileage depends in part on the speed of the car. The gas mileage of a subcompact car is given by... Problem 56PE: Gas mileage depends in part on the speed of the car. The gas mileage of a luxury car is given by L (... Problem 57PE: The Clostridium tetani bacterium is cultured to produce tetanus toxin used in an inactive form for... Problem 58PE: The bacterium Pseudomonas aeruginosa is cultured with an initial population of 10 4 active... Problem 59PE: For Exercises 59–64, use the standard form of a parabola given by to write an equation of a... Problem 60PE: For Exercises 59–64, use the standard form of a parabola given by to write an equation of a... Problem 61PE: For Exercises 59–64, use the standard form of a parabola given by y = a x 2 + b x + c to write an... Problem 62PE: For Exercises 59–64, use the standard form of a parabola given by y = a x 2 + b x + c to write an... Problem 63PE: For Exercises 59–64, use the standard form of a parabola given by y = a x 2 + b x + c to write an... Problem 64PE: For Exercises 59–64, use the standard form of a parabola given by y = a x 2 + b x + c to write an... Problem 65PE: A farmer wants to fence a rectangular corral adjacent to the side of a barn; however, she has only... Problem 66PE: A veterinarian wants to construct two equal-sized pens of maximum area out of 240 ft of fencing. See... Problem 67PE: For Exercises 67–72, graph the functions in Exercises 45–50 on a graphing calculator. Use the Max or... Problem 68PE: For Exercises 67–72, graph the functions in Exercises 45–50 on a graphing calculator. Use the Max or... Problem 69PE: For Exercises 67–72, graph the functions in Exercises 45–50 on a graphing calculator. Use the Max or... Problem 70PE: For Exercises 67–72, graph the functions in Exercises 45–50 on a graphing calculator. Use the Max or... Problem 71PE: For Exercises 67–72, graph the functions in Exercises 45–50 on a graphing calculator. Use the Max or... Problem 72PE: For Exercises 67–72, graph the functions in Exercises 45–50 on a graphing calculator. Use the Max or... format_list_bulleted