The graphs of the quadratic functions f x 6 10x and g x 8 x 2 2 are provided below Observe there are TWO lines simultaneously

Question

The graphs of the quadratic functions f x 6 10x and g x 8 x 2 2 are provided below Observe there are TWO lines simultaneously tangent to both graphs The one easier to imagine is tangent at points near the tops of the parabolas Place a ruler on the screen to see where it is approximately The other one should be on the left of the parabolas It is steeper and has a larger slope In this question you will find their equations You can start this question by setting the points of tangencies as a f a and b g b for example Then try to find equations hint slope involving the unknowns a and b 4 2 10 7 5 F2 5 5 7 5 10 a The line simultaneously tangent to both graphs having the LARGEST slope has equation Two decimal places of accuracy y x b The other line simultaneously tangent to both graphs has equation Two decimal places of accuracy Y x

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