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Math Help - Parabola question.... exam ..plz help asap..

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    Parabola question.... exam ..plz help asap..

    Write an equation of a quadratic functon that satisfies each set of condtions.

    a) the function has a minimum value of 6 at x=4.

    b) The parabola is congruent to y = 3x^2 and has a minimum value of 7.

    the answer for part a) y = 3(x-4)^2 + 6
    b) y = 3x^2+ 7

    these answers are from the back of my book.. it also says that "Answers may vary"... plz help me.. .thnx
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    is up to his old tricks again! Jhevon's Avatar
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    Quote Originally Posted by ruscutie100 View Post
    Write an equation of a quadratic functon that satisfies each set of condtions.

    a) the function has a minimum value of 6 at x=4.

    b) The parabola is congruent to y = 3x^2 and has a minimum value of 7.

    the answer for part a) y = 3(x-4)^2 + 6
    b) y = 3x^2+ 7

    these answers are from the back of my book.. it also says that "Answers may vary"... plz help me.. .thnx
    your answers seem fine to me
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    Quote Originally Posted by ruscutie100 View Post
    Write an equation of a quadratic functon that satisfies each set of condtions.

    a) the function has a minimum value of 6 at x=4.

    b) The parabola is congruent to y = 3x^2 and has a minimum value of 7.

    the answer for part a) y = 3(x-4)^2 + 6
    b) y = 3x^2+ 7

    these answers are from the back of my book.. it also says that "Answers may vary"... plz help me.. .thnx
    a) The (minimum) turning point is at (4, 6). You're familiar with the turning point form of a parabola - y = a(x - h)^2 + k where the turning point is at (h, k) - right?

    So any answer of the form y = a(x-4)^2 + 6, \, a > 0, \, satisfies the given property. The book chose a = 3. Other concrete answers can be got by choosing a = 1, 2, 4, 1/2, ......


    b) The turning point has y-coordinate y = 7. So k = 7 in the turning point form. In the turning point form, a 'controls the shape', so a = 3.

    So any answer of the form y = 3(x - h)^2 + 7 \, satisfies the given properties. The book chose h = 0, probably the simplest answer. Other concrete answers can be got by choosing h = 1, 2, 3, -1, -2 -3, 1/2, -1/2, ......
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    Quote Originally Posted by Jhevon View Post
    your answers seem fine to me
    That's because the answers are taken from the back of the book!
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    is up to his old tricks again! Jhevon's Avatar
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    Quote Originally Posted by mr fantastic View Post
    That's because the answers are taken from the back of the book!
    ah, yes, i see

    that's my line!
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    Quote Originally Posted by Jhevon View Post
    [snip]

    that's my line!
    Ah yes. But I learnt it from you
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    Quote Originally Posted by mr fantastic View Post
    a) The (minimum) turning point is at (4, 6). You're familiar with the turning point form of a parabola - y = a(x - h)^2 + k where the turning point is at (h, k) - right?

    So any answer of the form y = a(x-4)^2 + 6, \, a > 0, \, satisfies the given property. The book chose a = 3. Other concrete answers can be got by choosing a = 1, 2, 4, 1/2, ......


    b) The turning point has y-coordinate y = 7. So k = 7 in the turning point form. In the turning point form, a 'controls the shape', so a = 3.

    So any answer of the form y = 3(x - h)^2 + 7 \, satisfies the given properties. The book chose h = 0, probably the simplest answer. Other concrete answers can be got by choosing h = 1, 2, 3, -1, -2 -3, 1/2, -1/2, ......
    so i can pretty much put any value for a... thnx
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    Quote Originally Posted by ruscutie100 View Post
    so i can pretty much put any value for a... thnx
    Yes, as long as it's positive.
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