anonymous
  • anonymous
find an equation of the normal line to the parabola y=x^2-8x+9 at point (3,-6)... help me..
Mathematics
  • Stacey Warren - Expert brainly.com
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SOLVED
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katieb
  • katieb
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anonymous
  • anonymous
Can you use calculus?
anonymous
  • anonymous
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..
anonymous
  • anonymous
What do you get for y'(x) in general?

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anonymous
  • anonymous
i get 2x -8...
anonymous
  • anonymous
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.
anonymous
  • anonymous
More specifically, y'(x) gives you the 'slope' of the tangent at x.
anonymous
  • anonymous
so after that if i get the value of m,, should i substitute the (3,-6) again tu find c?
anonymous
  • anonymous
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?
anonymous
  • anonymous
so, it share the same value of x? right?
anonymous
  • anonymous
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).
anonymous
  • anonymous
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anonymous
  • anonymous
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.
anonymous
  • anonymous
ok i understand now...thanks for your explanation....
anonymous
  • anonymous
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).
anonymous
  • anonymous
but i little bit confuse,, how do u know the shape of graph was perpendicular?
anonymous
  • anonymous
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.
anonymous
  • anonymous
ok i understand..thank u,, :)

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