SOLUTION: . A quadratic function is defined by f (x) = −3.7x^2 + 6.8x + 4.3 . A linear function is defined by g(x) = −0.5x + k a) Determine the value of k so that the line inter

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Question 1090537: . A quadratic function is defined by f (x) = −3.7x^2 + 6.8x + 4.3 . A linear function is defined by g(x) = −0.5x + k
a) Determine the value of k so that the line intersects the parabola at exactly one point. Write your answer to the nearest hundredth.
b) Determine the values of k so that the line intersects the parabola at two points.
c) Determine the values of k so that the line never intersects the parabola.
Found 2 solutions by josgarithmetic, MathTherapy:
Answer by josgarithmetic(39617)   (Show Source): You can put this solution on YOUR website!





DISCRIMINANT,



A) One intersection


B) Two intersections



C) No intersections


Solve for k in each case.
Answer by MathTherapy(10552)   (Show Source): You can put this solution on YOUR website!
. A quadratic function is defined by f (x) = −3.7x^2 + 6.8x + 4.3 . A linear function is defined by g(x) = −0.5x + k
a) Determine the value of k so that the line intersects the parabola at exactly one point. Write your answer to the nearest hundredth.
b) Determine the values of k so that the line intersects the parabola at two points.
c) Determine the values of k so that the line never intersects the parabola. 
Hint: If a line intersects a parabola at EXACTLY one (1) point, that point WILL BE the VERTEX of the parabola. 

Therefore, find the vertex of the parabola by using the formula for the x-coordinate of the vertex of a parabola: .

Then substitute this x-value into the PARABOLIC equation to get the corresponding y-coordinate of the vertex. 

Substitute these PARABOLIC vertex-values: (h, k) as (x, y) into the linear function to get the value of k. 

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