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Adi3

  • one year ago

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

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  1. Adi3
    • one year ago
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    @SolomonZelman

  2. Adi3
    • one year ago
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    @AaronAndyson

  3. Adi3
    • one year ago
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    @imqwerty

  4. SolomonZelman
    • one year ago
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    \(\color{black}{ \displaystyle f(x)=2x^2+4~~~~\Longrightarrow ~~~~f(x)=2(x-0)^2+4 }\) And this is in the form of \(\color{black}{ \displaystyle f(x)=2(x-h)^2+k }\) (with vertex \((h,k)\) )

  5. Adi3
    • one year ago
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    ok so the vertex is 0,4

  6. SolomonZelman
    • one year ago
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    yes, correct.

  7. Adi3
    • one year ago
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    The vertex is min

  8. SolomonZelman
    • one year ago
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    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).

  9. SolomonZelman
    • one year ago
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    Yes, so the vertex is minimum.

  10. Adi3
    • one year ago
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    but you said max

  11. SolomonZelman
    • one year ago
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    When the leading coefficient is negative.

  12. Adi3
    • one year ago
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    ohh ok

  13. SolomonZelman
    • one year ago
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    But, as I said, when leading coefficient is positive (in your case it is 2), then the vertex is minimum.

  14. SolomonZelman
    • one year ago
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    And the range of the opening up parabola will start from the vertex, but has no restrictions on how large the output can be....

  15. Adi3
    • one year ago
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    so it is (y:y≤4)

  16. SolomonZelman
    • one year ago
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    Yes, that is exactly right.

  17. Adi3
    • one year ago
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    ??

  18. SolomonZelman
    • one year ago
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    Or, in interval notation \({\rm y} \in [4,+\infty)\)

  19. Adi3
    • one year ago
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    we did not learn that yet.

  20. SolomonZelman
    • one year ago
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    All that means is that the range goes from and including 4, and ends at positive infinity (meaning that it goes up forever endlessly).

  21. SolomonZelman
    • one year ago
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    don't want to throw in confusion.... in any case you are right y\(\le\)4.

  22. SolomonZelman
    • one year ago
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    Any questions about what we have done?

  23. Adi3
    • one year ago
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    nop, thanks a lot really apreciate, really needed it, i have a quiz tmrw.

  24. SolomonZelman
    • one year ago
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    Good luck on the quiz:)

  25. Adi3
    • one year ago
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    thanks mate

  26. Adi3
    • one year ago
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    thanks @imqwerty for seeing my question.

  27. imqwerty
    • one year ago
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    lolol XD

  28. Adi3
    • one year ago
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    lol

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