SOLUTION: hey, could u please solve this equation. find the quadratic relation in vertex form that has zeros -3 and 5 and passes through (3,6). i found x-value which is the axis of sym

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Question 113917: hey,
could u please solve this equation.
find the quadratic relation in vertex form that has zeros -3 and 5 and passes through (3,6).
i found x-value which is the axis of symmetry -3+5= 2/2 = 1
Therefore x=1
but i could not find the y-value
Please could u sovle it and send me back.
i will be waithing,
thank you,
Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!
Since the zeros are x=-3 and x=5 we can find the factorization using these zeros. We simply need to use the zero product property in reverse

x=-3 or x=5 Start with the given solutions

x%2B3=0 or x-5=0 Get the numbers to the left side

Since either piece equals zero, then their product equals zero

%28x%2B3%29%28x-5%29=0

However, this equation may not pass through (3,6). So let's introduce an "a" coefficient in front to get the equation:

y=a%28x%2B3%29%28x-5%29


Now since the equation passes through (3,6), this means x=3 and y=6


6=a%283%2B3%29%283-5%29 Plug in x=3 and y=6


6=a%286%29%28-2%29 Combine like terms


6=a%28-12%29 Multiply


6%2F%28-12%29=a Divide both sides by -12


-1%2F2=a Reduce


So our answer is a=-1%2F2 which means the equation is y=%28-1%2F2%29%28x%2B3%29%28x-5%29


Notice if we graph y=%28-1%2F2%29%28x%2B3%29%28x-5%29 and plot the point (3,6), we can see that the point lies on the line and y=%28-1%2F2%29%28x%2B3%29%28x-5%29 has zeros -3 and 5. So this verifies our answer.