SOLUTION: 1. let f be a quadratic function with a minimum value of -22100, a line of symmetry of x=140, and a y-intercept of (0,-2500). 2. the function g is the same as f but relfected

Algebra ->  Coordinate Systems and Linear Equations  -> Linear Equations and Systems Word Problems -> SOLUTION: 1. let f be a quadratic function with a minimum value of -22100, a line of symmetry of x=140, and a y-intercept of (0,-2500). 2. the function g is the same as f but relfected      Log On


   

Question 102: 1. let f be a quadratic function with a minimum value of -22100, a line of symmetry of x=140, and a y-intercept of (0,-2500).
2. the function g is the same as f but relfected about the x-axis and reduced by a factor of 200.
3. if x equals your grade, what is the value of g to one decimal place?
Answer by AnlytcPhil(1807) About Me  (Show Source):
You can put this solution on YOUR website!
1. let f be a quadratic function with a minimum value of

-22100, a line of symmetry of x=140, and a y-intercept of

(0,-2500).

2. the function g is the same as f but relfected about the

x-axis and reduced by a factor of 200.

3. if x equals your grade, what is the value of g to one decimal place?



>>...1. let f be a quadratic function...<<



f(x) = a(x-h)² + k



>>...with a minimum value of -22100,...<<



That tells us k = -22100, a > 0



So far we have



f(x) = a(x-h)² - 22100



>>...a line of symmetry of x=140, 



That tells us h = 140. So far we have



f(x) = a(x-140)² - 22100



>>...and a y-intercept of (0,-2500)...<<



That tells us f(0) = -2500. Substituting



-2500 = a(0-140)² - 22100 



19600 = 19600a



a = 1



So we now have



f(x) = 1(x-140)² - 22100



f(x) = (x-140)² - 22100



>>...2. the function g is the same as f but reflected about the

x-axis...<<



To reflect f(x) across the x-axis we multiply the right side

of its equation by -1



So far we have for the right side of g(x)



-[(x-140)² - 22100]



-(x-140)² + 22100 



>>...and reduced by a factor of 200...<<



That means to form the right side of g(x) we need to

multiply it by 1/200, or divide by 200:



[-(x-140)² + 22100]/200 or



-x²/200 + 7x/5 + 25/2



or



g(x) = -.005x² + 1.4x + 12.5



>>...3. if x equals your grade, what is the value of g to one

decimal place?...<<

You have to be given your grade.  Apparently this is a

teacher's function for curving grades.  Make a table of

values of possible grades, by substituting these values

of possible grades:  

If your grade is        Your curved grade is 

       x             g(x) = -.005x² + 1.4x + 12.5

      100            g(100) = 102.5

       90             g(90) = 98

       80             g(80) = 92.5

       70             g(70) = 86

       60             g(60) = 78.5

       50             g(50) = 70

       40             g(40) = 60.5

       30             g(30) = 50

       20             g(20) = 38.5

       10             g(10) = 26

        0              g(0) = 12.5        

   

If your grade is between two of these values, simply substitute

it for x in g(x) = -.005x² + 1.4x + 12.5 to get your curved grade.  



Edwin