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
Dima020 [189]
2 years ago
15

F(t)=t^2+19t+60 What are the zeros of the function and what is the vertex of the parabola?

Mathematics
1 answer:
SVEN [57.7K]2 years ago
4 0

Answer: -4,-15;\ \left(-\dfrac{19}{2},-\dfrac{121}{4}\right)

Step-by-step explanation:

Given

Function is F(t)=t^2+19+60

Zeroes of the function are

t^2+19t+60=0\\\\\Rightarrow t=\dfrac{-19\pm\sqrt{19^2-4\times 1\times 60}}{2\times 1}\\\\\Rightarrow t=\dfrac{-19\pm \sqrt{121}}{2}\\\\\Rightarrow t=\dfrac{-19\pm 11}{2}\\\\\Rightarrow t=-4,-15

Using completing the square method

y=t^2+2\times \dfrac{19}{2}t+\dfrac{19^2}{2^2}-\dfrac{19^2}{2^2}+60\\\\y=\left(t+\dfrac{19}{2}\right)^2+60-\dfrac{361}{4}\\\\y=\left(t+\dfrac{19}{2}\right)^2-\dfrac{121}{4}\\\\y+\dfrac{121}{4}=\left(t+\dfrac{19}{2}\right)^2\\\\\left(y-(-\dfrac{121}{4}\right)=\left(t-(-\dfrac{19}{2})\right)^2\\\\\text{The vertex is }\left(-\dfrac{19}{2},-\dfrac{121}{4}\right)

You might be interested in
pls help!? with all 4 Questions I would rlly appreciate your help thx to plp who help me I will improve on my math and be way be
aliina [53]
7.6=w/12
w=7.6(12)
w=91.2

x/2=20
x=20(2)
x=40

8.3x=41
x=41(8.3)
x=340.3

54=r/3
r=54(3)
r=162








6 0
3 years ago
-1^{2008} + (-1)^{2007} = ?<br><br> (1 - (-1)^[11])^[2] = ?<br><br> Questions for fun~
vladimir2022 [97]
1. -2
2. 4
Is the answers to the following questions
7 0
2 years ago
What is the answer to ...8.42 x 9
3241004551 [841]

Answer:

75.78

Step-by-step explanation:

8.42*9=75.78

6 0
3 years ago
Read 2 more answers
A square has a perimeter of 44. What is the length of side?
natka813 [3]
There are 4 sides on a square, and all 4 sides have the same length.
If the perimeter is 44, you would do 44/4.
44= permiter
4= number of sides
7 0
3 years ago
Read 2 more answers
At the skate park, an average of 126 bicycle per day are rented in October. This number is 10% less than the average number of b
OLga [1]
The answer is A which is 113. Hope this helped
4 0
3 years ago
Read 2 more answers
Other questions:
  • 3/4 of a number is 27. What’s the number?
    9·1 answer
  • What is the value of x <br><br> 24 <br> 9<br> 21<br> 14
    8·2 answers
  • Gini has a small garden that is 234 yards in length and 1 yard and with she grows roses 1/2 of her garden how many square yards
    10·1 answer
  • I need help im stuxk again and thanks who help me​
    7·1 answer
  • What is the numerical solution to the equation five less than three times a number equals four more than eight times the numbers
    12·1 answer
  • A car travels 312 miles in the same time that a motorcycle traveled 272. If the cars speed is 10mph more than the motorcycles, f
    14·1 answer
  • Two students, Abby and Melissa go for a walk. Abby begins walking 30 seconds earlier than Melissa .
    14·2 answers
  • Marco is 6 feet 3 inches tall. There are 2.54 centimeters in one inch. What is Marcos height in centimeters?
    12·1 answer
  • Graph the function.<br> g(x)=1/3(x-6)^2+1
    8·1 answer
  • Can I get help on this one
    14·2 answers
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!