SOLUTION: The function f(t) = t2 + 6t − 20 represents a parabola. Part A: Rewrite the function in vertex form by completing the square. Show your work. (6 points) Part B: Determi

Algebra ->  Quadratic Equations and Parabolas -> SOLUTION: The function f(t) = t2 + 6t − 20 represents a parabola. Part A: Rewrite the function in vertex form by completing the square. Show your work. (6 points) Part B: Determi      Log On


   

Question 980730: The function f(t) = t2 + 6t − 20 represents a parabola.
Part A: Rewrite the function in vertex form by completing the square. Show your work. (6 points)
Part B: Determine the vertex and indicate whether it is a maximum or a minimum on the graph. How do you know? (2 points)
Part C: Determine the axis of symmetry for f(t). (2 points)
Answer by MathLover1(20855) About Me  (Show Source):
You can put this solution on YOUR website!
f%28t%29+=+t%5E2+%2B+6t+-20
Part A: Rewrite the function in vertex form by completing the square.
f%28t%29+=+%28t%5E2+%2B+6t%2Bb%5E2%29-b%5E2+-20......recall that a%2Bb%29%5E2=a%5E2%2B2ab%2Bb%5E2, and compare it to f%28t%29+=+t%5E2+%2B+6t+-+20, you see that a=1 and 2ab=6; so, 2ab=6=>2%2A1b=6=>2b=6=>b=3
than we have
f%28t%29+=+%28t%5E2+%2B+6t%2B3%5E2%29-3%5E2+-+20
f%28t%29+=+%28t+%2B+3%29%5E2-9+-+20
f%28t%29+=+%28t+%2B+3%29%5E2+-29
Part B: Determine the vertex and indicate whether it is a maximum or a minimum on the graph.
compare f%28t%29+=+%28t+%2B+3%29%5E2+-29 to vertex form of parabola y=%28x-h%29%5E2%2Bk, you see that h=-3 and k=-29
so, the vertex is at:
(-3,-29)



Part C: Determine the axis of symmetry for f%28t%29

Every parabola has an axis of symmetry which is the line that runs down its 'center'. This line divides the graph into two perfect halves.
In the picture of on the left, the axis of symmetry is the line x+=+-3.