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
bezimeni [28]
2 years ago
14

Can someone please help me with my Question #29 of The Quadratic Relations for me please?

Mathematics
1 answer:
lara [203]2 years ago
7 0

Answer:

Calculate the <u>first differences</u> between the y-values:

\sf 3 \underset{+1}{\longrightarrow} 4 \underset{+3}{\longrightarrow} 7 \underset{+5}{\longrightarrow} 12 \underset{+7}{\longrightarrow} 19

As the first differences are <u>not the same</u>, we need to calculate the <u>second differences</u>:

\sf 1 \underset{+2}{\longrightarrow} 3 \underset{+2}{\longrightarrow} 5 \underset{+2}{\longrightarrow} 7

As the second differences are the <u>same</u>, the relationship between the variable is quadratic and will contain an x^2  term.

--------------------------------------------------------------------------------------------------

<u>To determine the quadratic equation</u>

The coefficient of x^2  is always <u>half</u> of the <u>second difference</u>.

As the second difference is 2, and half of 2 is 1, the coefficient of x^2 is 1.

The standard form of a quadratic equation is:  y=ax^2+bx+c

(where a, b and c are constants to be found).

We have already determined that the coefficient of x^2 is 1.

Therefore, a = 1

From the given table, when x=0, y=12.

\implies a(0)^2+b(0)+c=12

\implies c=12

Finally, to find b, substitute the found values of a and c into the equation, then substitute one of the ordered pairs from the given table:

\begin{aligned}\implies x^2+bx+12 & = y\\ \textsf{at }(1,19) \implies (1)^2+b(1)+12 & = 19\\ 1+b+12 & = 19\\b+13 & =19\\b&=6\end{aligned}

Therefore, the quadratic equation for the given ordered pairs is:

y=x^2+6x+12

You might be interested in
The differential equation dy dx equals the quotient of the quantity x plus 1 and y minus 3
Phantasy [73]

Answer:

I only

Step-by-step explanation:

dy/dx = x + 1 / y -3

(y - 3)dy = (x + 1) dx

integrate

1/2y^2 - 3x = 1/2x^2 + x

1/2y^2 = 1/2x^2 + 4x

y^2 = x^2 + 8x

y = (x^2 + 8x)^1/2

3 0
2 years ago
What are the factors PLEASE HELP!!!
elena55 [62]

Answer:

The answer is (x-6) squared

4 0
2 years ago
Simplify 4+1/2(24)=x^2
olga nikolaevna [1]
Answer x1 =-4 and x2=4

7 0
3 years ago
Read 2 more answers
Write as a repeating decimal using bar notation. Show your work.<br><br> 5/11
MrMuchimi
5/11
11 goes into 5 zero times (0.)
11 goes into 50 four times with a remainder of 6 (0.4)
11 goes into 60 five times with a remainder of 5 (0.45)
11 goes into 50 four times with a remainder of 6 (0.454)
11 goes into 60 five times with a remainder of 5 (0.4545)
The answer is .45 with a bar on top of both the 4 and the 5.
7 0
3 years ago
Undistribute the following:<br> 9x2 - 3x = _<br> _(3x-__)
dalvyx [7]

Answer:

3(-x+6)

Step-by-step explanation:

9x2-3x=18-3x

7 0
2 years ago
Other questions:
  • Adriano wants to get a new cell phone plan. Company A: $80 for a new phone in the monthly fee of $45 a month. Company B: she can
    5·1 answer
  • In your own words, write a definition for the word:<br><br>Base:
    9·1 answer
  • Ryan, Jessica, and Mark each solved this system of equations. All of their answers are different. Find and explain the mistakes.
    5·2 answers
  • What is 2x + 11y when x = 4 and y = 2?<br><br> A. 30<br><br> B. 38<br><br> C. 48<br><br> D. 136
    15·2 answers
  • Matrix bought a 5-pack of white t-shirts for 26 dollars what is the price per t-shirt
    11·2 answers
  • Can anyone help with this??
    12·1 answer
  • Which of the following is the equation of a line parallel to the line y = 4x + 1, passing throughout the point (5,1)?
    6·1 answer
  • Write your answer with no spaces and any fraction with “/“
    12·1 answer
  • James saved money regularly this year. He saved a
    6·1 answer
  • The circumference of a circle is 8cm. What is the diameter of a circle?
    11·2 answers
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!