1answer.
Ask question
Login Signup
Ask question
All categories
  • English
  • Mathematics
  • Social Studies
  • Business
  • History
  • Health
  • Geography
  • Biology
  • Physics
  • Chemistry
  • Computers and Technology
  • Arts
  • World Languages
  • Spanish
  • French
  • German
  • Advanced Placement (AP)
  • SAT
  • Medicine
  • Law
  • Engineering
Andrew [12]
3 years ago
12

The function f(t) = t2 + 6t − 20 represents a parabola.

Mathematics
2 answers:
NeX [460]3 years ago
4 0

Answer:

Step-by-step explanation:

Part A:

To complete the square, we will do the first few steps all at once, since they are necessary but not complicated to follow all at once.  Set the function equal to 0 first, then move the constant over to the other side:

t^2+6t=20

The most important rule for completing the square is that the leading coefficient (the number on the t-squared term) is a positive 1.  Ours is, but if it wasn't it would need to be factored out.

Next, take half the linear term, square it, and add it to both sides.  Our linear term is 6.  Half of 6 is 3, and 3 squared is 9, so we add 9 to both sides:

t^2+6t+9=20+9

On the right is simple addition, but on the left side, during this process we created a perfect square binomial that will reflect the h coordinate of the vertex.  We will state that binomial and do the addition on the right both at the same time:

(t+3)^2=38

If you FOIL out the (t + 3)(t + 3) you will get back the polynomial t^2+6t+9

Now we can move the constant back over and set the polynomial back to equal f(t):

(t+3)^2-38=f(t)

From this we determine the vertex to sit at (-3, -38)

Part B:

Because this is a positive parabola that opens upwards, the function will have a minimum value (if it was negative and opened upside down, it would have a minimum value).  In other words, you know the vertex is a minimum because this is a positive parabola that opens upwards.

Part C:

The axis of symmetry is the line that cuts the parabola in half, creating 2 identical, mirror images.  Because this parabola opens upwards, a vertical line is required to cut it into 2 identical halves.  The vertical line has an equation " x = ".  In the case of a positive parabola that opens upwards, the line of symmetry, what x = , will ALWAYS be the number that is inside the parenthesis with the x.  Since the standard vertex form is

f(t)=(t-h)^2+k

our vertex can be rewritten as (t - (-3)).  Therefore, our axis of symmetry is

x = -3

MatroZZZ [7]3 years ago
4 0

Answer: Got a 100% with this answer:

f(x)=ax²+bx+c. a= 1, b= 6, and c= -20.

To write a quadratic in vertex form, first take half of the b value and square it: (6/2)² = 3² = 9. This is what we will add and subtract to the function:

f(t) = t²+6t+9-20-9

The squared portion will be (t+b/2)²:

f(t) = (t+3)²-20-9

f(t) = (t+3)²-29

 

Part B:   Vertex form = f(x) = a(x-h)²+k, where (h, k) is the vertex; and in the function, (h, k) is (-3, -29). The vertex is a minimum because this is a positive parabola that opens down.  

Part C: Axis of symmetry is t=h, therefore axis of symmetry is t=-3 or -3.

You might be interested in
Determine x if f(x)=60 explain your choice.
mihalych1998 [28]

Answer:

x=60

Step-by-step explanation:

since f(x) =60 then y is f(x) and in the form y=x 60 is x

3 0
2 years ago
Is it true or false
3241004551 [841]

True.

I hope this helps you

7 0
2 years ago
Read 2 more answers
50 points please help ASAP!!!!!
ladessa [460]

Answer:

So your learning probability

The answer is B

7 0
3 years ago
five hotdogs cost $1.80.Each hotdog cost the same amount.What is the cost per hotdog in dollars and cents
earnstyle [38]

Answer:

$0.36

Step-by-step explanation:

3 0
3 years ago
Read 2 more answers
Need help asap<br> will give brain
SCORPION-xisa [38]
Question 1 is F question 2 is D
4 0
2 years ago
Read 2 more answers
Other questions:
  • Find the product 12.34.0.74.91
    12·2 answers
  • The local jewelry store marks up the price of a necklace by 65% before selling them. If the store paid the distributor $85 per n
    12·1 answer
  • Find all solutions of the equation in the interval [0,2π) sec(theta) +2=0
    9·1 answer
  • In the land of Ink, the money system is unique. One Trinket is equal to 4 Blinkets, and 3 Blinkets are equal to 7 Drinkets. In T
    11·2 answers
  • if the wheel of the engine of a train is 30/7m in circumference and makes 7 revolutions in 4 secs then the speed of the train is
    10·1 answer
  • What is the answer or how do I solve this
    7·2 answers
  • Please help me with these 19 and 20 and tell me what you use to get the answer
    9·2 answers
  • juan worked 2.5 hours each day from monday through friday plus 7.5 hours on saturday. his total pay was 128 dollars. how much di
    12·1 answer
  • The assignment is in the picture below, provided with instructions.
    6·2 answers
  • Use logarithm table to solve (0.7634)^4​
    5·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!