Question 1042755: Write the equation of the quadratic function with roots -9 and and -3 and a vertex at (-6, -1)
Help please! Answer by ikleyn(52777) (Show Source):
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Write the equation of the quadratic function with roots -9 and and -3 and a vertex at (-6, -1)
Help please!
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I know (and you should know it) that this function has a form
f(x) = a*(x-(-9)*(x-(-3)) = a*(x+9)*(x+3),
where "a" is a real constant.
To determine this constant, I will calculate the function f(x) at the point x = -6, where the vertex is. It is
f(-6) = a*(-6 +9)*(-6+3) = a*3*(-3) = -9a.
Thus, I must find the value of "a" from this equation:
f(-6) = -1, which becomes -9a = -1.
Hence, a = = .
Answer. The function under the question is f(x) = .
You may open parentheses if you need.
