Adi3
  • Adi3
for each of the following quadratic functions: (i) Find the coordinates for the vertex (ii) determine whether the vertex is max or min (iii) find the range for the functions (a) f(x) = 2x^2 +4
Mathematics
  • Stacey Warren - Expert brainly.com
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SOLVED
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chestercat
  • chestercat
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Adi3
  • Adi3
@SolomonZelman
Adi3
  • Adi3
@AaronAndyson
Adi3
  • Adi3
@imqwerty

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More answers

SolomonZelman
  • SolomonZelman
\(\color{black}{ \displaystyle f(x)=2x^2+4~~~~\Longrightarrow ~~~~f(x)=2(x-0)^2+4 }\) And this is in the form of \(\color{black}{ \displaystyle f(x)=2(x-h)^2+k }\) (with vertex \((h,k)\) )
Adi3
  • Adi3
ok so the vertex is 0,4
SolomonZelman
  • SolomonZelman
yes, correct.
Adi3
  • Adi3
The vertex is min
SolomonZelman
  • SolomonZelman
If the leading coefficient is POSITIVE, then parabola opens UP, the vertex is the MINIMUM point (or the absolute MINIMUM). If the leading coefficient is NEGATIVE, then parabola opens DOWN, the vertex is the MAXIMUM point (or the absolute MAXIMUM).
SolomonZelman
  • SolomonZelman
Yes, so the vertex is minimum.
Adi3
  • Adi3
but you said max
SolomonZelman
  • SolomonZelman
When the leading coefficient is negative.
Adi3
  • Adi3
ohh ok
SolomonZelman
  • SolomonZelman
But, as I said, when leading coefficient is positive (in your case it is 2), then the vertex is minimum.
SolomonZelman
  • SolomonZelman
And the range of the opening up parabola will start from the vertex, but has no restrictions on how large the output can be....
Adi3
  • Adi3
so it is (y:y≤4)
SolomonZelman
  • SolomonZelman
Yes, that is exactly right.
Adi3
  • Adi3
??
SolomonZelman
  • SolomonZelman
Or, in interval notation \({\rm y} \in [4,+\infty)\)
Adi3
  • Adi3
we did not learn that yet.
SolomonZelman
  • SolomonZelman
All that means is that the range goes from and including 4, and ends at positive infinity (meaning that it goes up forever endlessly).
SolomonZelman
  • SolomonZelman
don't want to throw in confusion.... in any case you are right y\(\le\)4.
SolomonZelman
  • SolomonZelman
Any questions about what we have done?
Adi3
  • Adi3
nop, thanks a lot really apreciate, really needed it, i have a quiz tmrw.
SolomonZelman
  • SolomonZelman
Good luck on the quiz:)
Adi3
  • Adi3
thanks mate
Adi3
  • Adi3
thanks @imqwerty for seeing my question.
imqwerty
  • imqwerty
lolol XD
Adi3
  • Adi3
lol

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