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sha0403

  • 2 years ago

find an equation of the normal line to the parabola y=x^2-8x+9 at point (3,-6)... help me..

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  1. LogicalApple
    • 2 years ago
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    Can you use calculus?

  2. sha0403
    • 2 years ago
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    how to use it? i don't know coz it do not give the value of x after differetiate.. so i don't know how to find m..

  3. LogicalApple
    • 2 years ago
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    What do you get for y'(x) in general?

  4. sha0403
    • 2 years ago
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    i get 2x -8...

  5. LogicalApple
    • 2 years ago
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    Perfect. This is the equation of the tangents of x^2 - 8x + 9. Let x = 3 and solve for y'(x) to get the tangent at that point.

  6. LogicalApple
    • 2 years ago
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    More specifically, y'(x) gives you the 'slope' of the tangent at x.

  7. sha0403
    • 2 years ago
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    so after that if i get the value of m,, should i substitute the (3,-6) again tu find c?

  8. LogicalApple
    • 2 years ago
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    Let's assume you found the slope at x = 3. This is the slope of the tangent line. The slope of the normal line would be perpendicular to it. What is the relationship of slopes between perpendicular lines?

  9. sha0403
    • 2 years ago
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    so, it share the same value of x? right?

  10. LogicalApple
    • 2 years ago
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    Well, the point (3, -6) will be the same. The only difference is, the slope of the normal line will be the negative reciprocal of the slope of the tangent line (since they are perpendicular).

  11. LogicalApple
    • 2 years ago
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    |dw:1356835091005:dw|

  12. LogicalApple
    • 2 years ago
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    The point there is supposed to represent (3, -6). The tangent line is drawn with a slope of m = y'(3), and the normal line is also drawn perpendicular to it.

  13. sha0403
    • 2 years ago
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    ok i understand now...thanks for your explanation....

  14. LogicalApple
    • 2 years ago
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    y'(3) = 2(3) - 8 = -2 = slope of the tangent line Thus the slope of the normal line would be 1/2 and pass through (3, -6).

  15. sha0403
    • 2 years ago
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    but i little bit confuse,, how do u know the shape of graph was perpendicular?

  16. LogicalApple
    • 2 years ago
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    Do you mean the direction of the normal line? A normal line is just a line perpendicular to whatever shape we're talking about. More specifically, a normal line is perpendicular to a tangent line.

  17. sha0403
    • 2 years ago
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    ok i understand..thank u,, :)

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