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Here is my question

The quadratic function $f$ is negative only on the open interval $(−2, 1/4 )$ and its graph passes through the point$ (−1, −5)$. Determine the coefficients of f and sketch its graph.

Please explain how you got your answer and thank you.

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1 Answer 1

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$f(x)=\kappa(x+2)(x-\frac{1}{4})$ then $f(-1)=-5$ to deduce $\kappa$

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  • $\begingroup$ Please explain what the question means. Can you please provide more detail? Also, I need to know all 3 coefficients, not just one.Thanks $\endgroup$
    – Dylan Ong
    Feb 2, 2019 at 21:41
  • $\begingroup$ $f$ is quadratic and change sign at $-2$ and $\frac{1}{4}$ therefore the two values are roots of $f$ and the claim follows. $\endgroup$
    – DINEDINE
    Feb 2, 2019 at 21:46
  • $\begingroup$ I am a beginner. Please explain more. Thanks $\endgroup$
    – Dylan Ong
    Feb 2, 2019 at 21:49
  • $\begingroup$ Look, can you trip from Los Angeles to Paris without crossing water? Los Angeles is the positive sign, Paris the negative and water is the « zero ». Since your function is positive before -2 and negative after -2, so $f(-2)=0$, hence it must be a (x-(-2)) as a factor of f. Same argument at 1/4. You must know that every quadratic function can be written as a(x-root1)(x-root2). $\endgroup$
    – DINEDINE
    Feb 2, 2019 at 21:59
  • $\begingroup$ Thank you for your explanation. I still wonder how I can get the other two. $\endgroup$
    – Dylan Ong
    Feb 2, 2019 at 22:21

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