Find an equation of the quadratic function with zeros at (0,0) and (6,0) with f ( 5 ) = − 15write the equation of the quadratic function with zeros at (0,0) and (6,0) with f ( 5 ) = − 15So, I know how to get the equation from the zeros, but I am confused with what I am supposed to do with " f ( 5 ) = − 15".

Question

Find an equation of the quadratic function with zeros at (0,0) and (6,0) with   f  (  5  )  =  −  15write the equation of the quadratic function with zeros at (0,0) and (6,0) with   f  (  5  )  =  −  15So, I know how to get the equation from the zeros, but I am confused with what I am supposed to do with &quot;  f  (  5  )  =  −  15&quot;.

Marshall Flowers · Accepted Answer

Step 1You are given that the roots are (0,0) and (6,0). This means that if if   f  (  x  )  =  a      x    2    +  b  x  +  c, then you can write   f  (  0  )  =  0 and   f  (  6  )  =  0 you are also given   f  (  5  )  =  −  15.We have   f  (  0  )  =  c  =  0. Hence, can write   f  (  x  )  =  a      x    2    +  b  x. We still need to find a and b. Since   f  (  6  )  =  0  , we have   36  a  +  6  b  =  0. And since   f  (  5  )  =  −  15  , then   25  a  +  5  b  =  −  15 which means (after simplifying)   5  a  +  b  =  −  3. Solve this for b to obtain   b  =  −  3  −  5  a. Substitute this into   36  a  +  6  b  =  0, to obtainStep 2  36  a  +  6  (  −  3  −  5  a  )  =  0    ⟹    36  a  −  18  −  30  a  =  0    ⟹    6  a  =  18    ⟹    a  =  3and putting this into   b  =  −  3  −  5  a, we obtain that   b  =  −  3  −  5  (  3  )  =  −  18. In other words,                               f          (          x          )          =          3                      x            2                    −          18          x

Find an equation of the quadratic function with zeros at (0,0) and (6,0) with f(5)=-15

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