find 2nd degree polynomial f(x) = ax^2+bx+c such that its graph has a tangent line with slope=6 @ point(-2, 7) and x-int @ (-1, 0).
We can use the points we know to find a system of equations
Since we know the derivative represents slope we know when x=-2 that so we get
Now using the point (-2,7) in f(x) we get
and the point (-1,0) we get
We now have a system of equations in a,b, and c
Multiplying 3 by -1 and adding it to 2 gives
Now if add equation one to this one we get
Plugging this in above gives
Now putting a and b into equation 3 gives
So we get
I hope this helps.
Hello, weezie23!
Find a 2nd degree polynomial: such that its graph
has a tangent line with slope = 6 at point(-2, 7) and x-int (-1, 0)
We have: . .and we must find
The point (-2,7) is on the graph.
. .
The point (-1,0) is on the graph.
. .
When , the slope is 6.
We have: .
. .
Solve the system of equations: .
And we have: .
Substitute into [3]: .
Substitute into [2]: .
Therefore: .