SOLUTION: Determine the quadratic function that has the given roots and passes through the given point. Express each function in standard form. (10 marks: 5 marks each) a) x = 2 ± √5, (2,

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Question 1194305: Determine the quadratic function that has the given roots and passes through the given point. Express each function in standard form. (10 marks: 5 marks each) a) x = 2 ± √5, (2, 10)
Found 3 solutions by ikleyn, Alan3354, greenestamps:
Answer by ikleyn(52780)   (Show Source): You can put this solution on YOUR website!
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Determine the quadratic function that has the given roots and passes through the given point.
Express each function in standard form. (10 marks: 5 marks each) a) x = 2 ± √5, (2, 10)
~~~~~~~~~~~~~~ 

Having given these roots, you can write the quadratic function as the product of linear binomials

    f(x) = ,

where factor  " a " is a real number.


Simplify this expression

    f(x) =  =  =  = .


Now your task is to find the value of the coefficient "a".

For it, use the condition that f(2) = 10, given in the problem.

It gives you this equation

     = 10,

    a*(4 - 8 - 1) = 10,

    -5a           = 10

     a            = 10/(-5) = -2.


So, the quadratic function is  f(x) = -2*(x^2-4x-1).      ANSWER

Solved and explained.



Answer by Alan3354(69443)   (Show Source): You can put this solution on YOUR website!
We don't need to know that # of marks.
Answer by greenestamps(13200)   (Show Source): You can put this solution on YOUR website!


An alternative path to the answer is using Vieta's theorem with the two given roots.

The sum of the given roots is 4; the product is -1. So the function is of the form



The constant a is determined by the given point.





ANSWER: The function is or


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