SOLUTION: Find the value for c such that y = x + c is a tangent to the parabola y = x^2-x-12. Can you please help me do questions like that? What is meant by 'tangent to the parabola'?

Algebra ->  Quadratic Equations and Parabolas  -> Quadratic Equation Customizable Word Problems -> SOLUTION: Find the value for c such that y = x + c is a tangent to the parabola y = x^2-x-12. Can you please help me do questions like that? What is meant by 'tangent to the parabola'?       Log On


   

Question 1114498: Find the value for c such that y = x + c is a tangent to the parabola
y = x^2-x-12.
Can you please help me do questions like that? What is meant by 'tangent to the parabola'?
Thankyou
Answer by josgarithmetic(39613) About Me  (Show Source):
You can put this solution on YOUR website!
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What is meant by 'tangent to the parabola'?
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The line which touches but does not cross the parabola at the particular local point.

y+=+x%5E2-x-12
-
dx%2Fdy=2x-1
Slope of a tangent line to the parabola is 2x-1.

y=mx%2Bc=%282x-1%29x%2Bc=1%2Ax%2Bc
meaning, 2x-1=1
2x=2
x=1

The point on the parabola for x=1 is
y=x%5E2-x-12
y=1-1-12
y=-12


This point (1,-12) is both on the parabola and also on the line y=x%2Bc.
c=y-x
c=-12-1
highlight%28c=-13%29


The tangent line at that point:
highlight%28y=x-13%29
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graph%28300%2C300%2C-7%2C7%2C-13%2C1%2Cx%5E2-x-12%2Cx-13%29