Question 885645: find the equation, in factored form, of the quadratic function with zeros -3 and -7 that passes through the point (-5, 4)
Answer by Theo(13342)   (Show Source):
You can put this solution on YOUR website! if the zeroes are -3 and -7, you can find the factors by doing the following:
first zero:
x = -3
add 3 to both sides of this equation to get:
x + 3 = 0
second zero:
x = -7
add 7 to both sides of this equation to get:
x + 7 = 0
so far your factors are:
(x + 3) * (x + 7)
put these factors into equation form and you get:
f(x) = (x + 3) * (x + 7)
since the equation goes through the point (-5,4), then when x = -4 you should get f(x) = -5.
replacing x with -5, you get f(x) (-5 + 3) * (-5 + 7) which is equal to (-2) * (2) which is equal to (-4).
this is the right value but the wrong sign.
what this means is you need another factor of (-1) to make sure you get the right value.
your factors become:
f(x) = (-1) * (x + 3) * (x + 7)
now when you replace x with -5, you get f(x) = (-1) * (-2) * (2) which is equal to (-1) * (-4) which is equal to 4.
your factors are:
(-1) * (x + 3) * (x + 7)
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