donnie1999
  • donnie1999
Determine in which direction the parabola below opens. y = -2x^2 + 5x - 2
Mathematics
schrodinger
  • schrodinger
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donnie1999
  • donnie1999
SolomonZelman
  • SolomonZelman
Ok, here: ~ b and c can be any negative or positive real numbers (or can be zero). ~ a is a positive number that can't be equal to zero (and thus -a is a negative number) `----------------------------` `UP/DOWN opening parabolas.` If you have \(\large\color{black}{ \displaystyle y=ax^2+bx+c }\) then, this parabola opens UP If you have \(\large\color{black}{ \displaystyle y=-ax^2+bx+c }\) then, this parabola opens DOWN `LEFT/RIGHT opening parabolas.` If you have \(\large\color{black}{ \displaystyle x=-ay^2+by+c }\) then, this parabola opens to the LEFT If you have \(\large\color{black}{ \displaystyle x=ay^2+by+c }\) then, this parabola opens to the RIGHT
SolomonZelman
  • SolomonZelman
do you want some real (not abstract) examples?

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donnie1999
  • donnie1999
Im confused so the answer is right???
anonymous
  • anonymous
here is some help
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some.random.cool.kid
  • some.random.cool.kid
yeah don those were what I meant his examples is a negative the other one was positive.
donnie1999
  • donnie1999
ohh so am i correct in saying that the answer is UP?
SolomonZelman
  • SolomonZelman
yes
SolomonZelman
  • SolomonZelman
I will give you some examples. OPENS UP (examples) \(\large\color{black}{ \displaystyle y=x^2-4x+2 }\) \(\large\color{black}{ \displaystyle y=0.2x^2-18 }\) \(\large\color{black}{ \displaystyle y=19x^2+6x }\) \(\large\color{black}{ \displaystyle y=3x^2+3x+3 }\) (as long as that number in front of x² is positive) OPENS DOWN (examples) \(\large\color{black}{ \displaystyle y=-x^2 }\) \(\large\color{black}{ \displaystyle y=-0.01x^2+200 }\) \(\large\color{black}{ \displaystyle y=-9x^2-17x }\) \(\large\color{black}{ \displaystyle y=-5x^2+3x-7 }\) (as long as that number in front of x² is negative)

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