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Just For Fun - Parabolas

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Prove that if  a tangent line is drawn to the parabola y = x^2 at the point x = a.......then the line will have a y-intercept of ( 0, -a^2 )

CPhill  Dec 3, 2016

#2
+10613
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Parabola   y = x^2

when x= a    y = a^2

Slope = 2x    (derivative of x^2)

y=mx+b   yields    a^2 = 2a(a) + b

a^2 = 2a^2 + b

0 = a^2 + b

b= -a^2

so   y = mx + b becomes        y = 2x(x) - a^2            When x = 0   y = - a^2

Yah?

ElectricPavlov  Dec 4, 2016
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#1
+90127
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Pick me .....   Pick. me ...      LOL

Melody  Dec 4, 2016
#2
+10613
+11

Parabola   y = x^2

when x= a    y = a^2

Slope = 2x    (derivative of x^2)

y=mx+b   yields    a^2 = 2a(a) + b

a^2 = 2a^2 + b

0 = a^2 + b

b= -a^2

so   y = mx + b becomes        y = 2x(x) - a^2            When x = 0   y = - a^2

Yah?

ElectricPavlov  Dec 4, 2016

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