SOLUTION: Find the y-intercept of the line with gradient -3 that is tangential to the parabola y = 2x^2-5x + 1.

Algebra ->  Quadratic Equations and Parabolas  -> Quadratic Equations Lessons  -> Quadratic Equation Lesson -> SOLUTION: Find the y-intercept of the line with gradient -3 that is tangential to the parabola y = 2x^2-5x + 1.      Log On


   

Question 1092312: Find the y-intercept of the line with gradient -3 that is tangential to the parabola
y = 2x^2-5x + 1.
Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
Find the derivative y'
+y%5B1%5D+=+4x+-+5+
You are given y' = -3
+4x+-+5+=+-3+
+4x+=+2+
+x+=+1%2F2+
Now find +y+ on the parabola
where slope = +-3+
+y+=+2%2A%281%2F2%29%5E2+-+5%2A%281%2F2%29+%2B+1+
+y+=+1%2F2+-+5%2F2+%2B+2%2F2+
+y+=+-1+
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The line is tangent to the parabola at the point ( 1/2, -1 )
The slope intercept form is:
+y+=+m%2Ax+%2B+b+
where +b+ is the y-intercept
+-1+=+%28-3%29%2A%281%2F2%29+%2B+b+
+-1+=+-3%2F2+%2B+b+
+b+=+1%2F2+
The y-intercept is at ( 0, 1/2 )
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Check:
Here's the plot of parabola and straight line:
+graph%28+400%2C+400%2C+-6%2C+6%2C+-6%2C+6%2C+2x%5E2+-+5x+%2B+1%2C+-3x+%2B+1%2F2+%29+