SOLUTION: HI can someone please help me out with this question? you don't have to answer everything if you don't want to. anything helps. thank you so much A quadratic function is defined b

Algebra ->  Quadratic Equations and Parabolas  -> Quadratic Equations Lessons  -> Quadratic Equation Lesson -> SOLUTION: HI can someone please help me out with this question? you don't have to answer everything if you don't want to. anything helps. thank you so much A quadratic function is defined b      Log On


   

Question 1090556: HI can someone please help me out with this question? you don't have to answer everything if you don't want to. anything helps. thank you so much
A quadratic function is defined by f(x)=-3.7x^2+6.8x+4.2. A linear function is defined by g(x) = –0.5x + k.
a) Determine the A quadratic function is defined by . A linear function is defined by g(x) = –0.5x + k. 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.
Answer by greenestamps(13200) About Me  (Show Source):
You can put this solution on YOUR website!

Set the two functions equal to each other to find where they intersect. You end up with a quadratic function that involves the parameter k.

-3.7x%5E2%2B6.8x%2B4.2+=+-0.5x+%2B+k
-3.7x%5E2%2B7.3x%2B%284.2-k%29+=+0

You want the parabola and the line to intersect at exactly one point. That means you want this quadratic equation to have a single solution. It has a single solution when the discriminant in the quadratic formula,
b%5E2-4ac
is equal to 0. So solve for k:
%287.3%29%5E2+-+4%28-3.7%29%284.2-k%29=0

I will let you finish that part... since you said it was okay if I didn't answer everything. Besides, you will learn more from this if you do some of the work yourself.

Then answering the other two questions is easy.

Since k is the y-intercept of the linear function, and since the parabola opens downward, any value of k smaller than the one that gives a single intersection point will give 2 intersection points, and any value larger will give 0 intersection points.