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. 
<pre>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: {{{x = - b/(2a)}}}.
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.