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anonymous

  • 5 years ago

A frog leaps from a stump 4 feet high and lands 6 feet from teh base of the stump. we can consider the initial position of the frog to be (0,4) and its landing to be (6,0). the height of the frog in feet is given by the following equation: -1/3x^2+4/3x+4 1. what is the horizontal distance (x) from the base of the stump when the frog reached maximum height? 2. what was the maximum height

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  1. anonymous
    • 5 years ago
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    The maximum height is found at the vertex of the parabola. You have a parabola when you have an x^2 term as the highest degree. The vertex is found at -b/2a this happen to be the horizontal distance. what would -b/2a be?

  2. anonymous
    • 5 years ago
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    Are you in Algebra or Calculus? This is an algebraic way of doing it.

  3. anonymous
    • 5 years ago
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    algebra

  4. anonymous
    • 5 years ago
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    OK.. so let's do it this way. a = -1/3 b = 4/3 -b/2a = -4/3 over -2/3 ok so far?

  5. anonymous
    • 5 years ago
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    ok got ya

  6. anonymous
    • 5 years ago
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    When you divide by a fraction, you multiply by the reciprocal. -4/3 * -3/2 = 12/6 = 2 so x = 2 that is how far away from the stump you are when the the frog is at it's maximum

  7. anonymous
    • 5 years ago
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    so the vetex is 2 and thats the horizontal distance?

  8. anonymous
    • 5 years ago
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    f f f f f s f f --------- f-------------ground ^ x = 2

  9. anonymous
    • 5 years ago
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    Does my picture make sense... kind of dumb I know

  10. anonymous
    • 5 years ago
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    no that really helps

  11. anonymous
    • 5 years ago
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    The x value of the vertex is 2 and that is the horizontal distance, now we need to find how high it is at x = 2 Substitute 2 into your equation and find y

  12. anonymous
    • 5 years ago
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    y=5.3?

  13. anonymous
    • 5 years ago
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    or is it y=8

  14. anonymous
    • 5 years ago
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    y = 5.3 I think... (-1/3)*4 + (4/3)*2 +4 -4/3 + 8/3 + 4 4/3 + 4 5 1/3 Notice the vertex (which is the highest point) has coordinates (2,5.3)

  15. anonymous
    • 5 years ago
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    ok think i got ya

  16. anonymous
    • 5 years ago
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    ok think i got ya

  17. anonymous
    • 5 years ago
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    how would u sketch a graph of this problem

  18. anonymous
    • 5 years ago
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    Use your xy coordinate graph paper. put a dot on (0,4) that is the frog. Put a dot on (6,0) that is where the frog lands Put a dot on (2,5.3) that is the highest point. Draw an arc "like throwing a ball up in the air" to the highest point and then down to the (6,0) point. Like a ball would look like if you were throwing it.

  19. anonymous
    • 5 years ago
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    ok thank u i thought it would be an arc

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