iwanttogotostanford
  • iwanttogotostanford
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Mathematics
  • Stacey Warren - Expert brainly.com
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schrodinger
  • schrodinger
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iwanttogotostanford
  • iwanttogotostanford
@Cardinal_Carlo
anonymous
  • anonymous
A downward quadratic function is when its curve resembles a frown face. This also means that the a-value in f(x) = ax^2 is negative (or <0 as mathematically noted). So: \[f(x) = x ^{2} ~~~is ~~positive ~(+) ~~or ~~upward \left( \smile \right)\] To make this quadratic function negative, we just have to multiply to a negative value which in our case is k = -1. \[f(x) \times k = x ^{2} \times \left( -1 \right) = -x ^{2}\] \[f(x) = -x ^{2}\] \[f(x) ~~~is ~~now ~~negative \left( - \right) ~~or ~~downward ~~(\frown)\]
iwanttogotostanford
  • iwanttogotostanford
@Cardinal_Carlo I'm still confused, would it be f(kx) then?

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anonymous
  • anonymous
Well if we did f(kx), we would get: \[f(x) = x ^{2}\] \[f(kx) = \left( kx \right)^{2} = \left( -x \right)^{2} = x ^{2}\] As you can see, -1 will always become a positive 1 after it's squared. This is not our answer.
iwanttogotostanford
  • iwanttogotostanford
oh ok
anonymous
  • anonymous
Your actual answer is kf(x) which is basically the product of k and f(x). From this, we get: \[kf(x) = \left( -1 \right)x ^{2} = -x ^{2}\] which is what we need to make f(x) negative. Is this making any sense so far?

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