SOLUTION: A quadratic function has roots 3 and - 5, which passes through the point (1, 5). Under what conditions will it intersect with a line of slope -4 once? Twice? Never?
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Question 1188454: A quadratic function has roots 3 and - 5, which passes through the point (1, 5). Under what conditions will it intersect with a line of slope -4 once? Twice? Never?
Answer by Solver92311(821) (Show Source): You can put this solution on YOUR website!
Sunday, April 2, 2017
7:06 PM
Quadratic with roots 3 and -5 that passes through (1,5).
\ =\ a(x\,-\,3)(x\,+\,5))
\ =\ a(-2)(6)\ =\ 5)
Hence 
and
\ =\ -\frac{5}{12}x^2\ -\ \frac{5}{6}x\ +\ \frac{25}{4})
Set the first derivative equal to -4 and solve:
)
All lines with slope -4 have an equation of the form \ +\ \rho(x_1))
. Since a line with a slope of -4 is tangent to the graph of the quadratic function at the point \))
, or )
, the line \ -\ \frac{44}{15})
intersects the function graph exactly once. Any line of the form where 
will not intersect the function graph anywhere. And where 
, the line will intersect the function graph in two places.
John
My calculator said it, I believe it, that settles it
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