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77julia77 [94]
3 years ago
13

Write the equation of the quadratic function that passes through the points (-1, 1), (1, 5), and (2,10).

Mathematics
1 answer:
Serjik [45]3 years ago
6 0

Answer:

\displaystyle f(x)=x^2+2x+2

Step-by-step explanation:

<u>System Of Linear Equations </u>

In this problem, we'll need to solve a 3x3 system of linear equations because we have three unknowns and three conditions.

We are required to find the equation of the quadratic function that passes through the points (-1, 1), (1, 5), and (2,10)

The general quadratic function can be written as

\displaystyle f(x)=ax^2+bx+c

We need to find the values of a,b, and c. Let's use the first condition, i.e. f(-1)=1

\displaystyle f(-1)=a(-1)^2+b(-1)+c

\displaystyle f(-1)=a-b+c

\displaystyle a-b+c=1.....[eq\ 1]

Now we use the second condition f(1)=5

\displaystyle f(1)=a(1)^2+b(1)+c

\displaystyle f(1)=a+b+c

\displaystyle a+b+c=5.......[eq\ 2]

Finally, we use the third condition f(2)=10

\displaystyle f(2)=a(2)^2+b(2)+c

\displaystyle f(2)=4a+2b+c

\displaystyle 4a+2b+c=10....[eq\ 3]

We put together eq 1, eq 2, and eq 3 to form the system

\displaystyle \left\{\begin{matrix}a-b+c=1\\ a+b+c=5\\ 4a+2b+c=10\end{matrix}\right.

Adding the first two equations we have

\displaystyle 2a+2c=6

\displaystyle a+c=3

And also

\displaystyle b=2

Using the above equation and the value of b in the third equation, we have

\displaystyle \left\{\begin{matrix}a+c=3\\ 4a+c=6\end{matrix}\right.

Subtracting the first equation from the second

\displaystyle 3a=3

\displaystyle a=1

And therefore

\displaystyle c=2

Now we have all the values, the quadratic function is

\displaystyle \boxed{f(x)=x^2+2x+2}

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Step-by-step explanation:

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2 years ago
Which of the following is an equation of the line that crosses through (-3,4) and (3,6)?
Mama L [17]

Answer:

y=(1/3)x+5

Step-by-step explanation:

Slope-intercept: y=mx+b

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plug in one of the points (3,6)

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3 years ago
9.4 the tangent ratio<br> please help on #27 and 28
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Answer/Step-by-step explanation:

27.

✔️Sin 23 = opp/hyp

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28.

✔️Sin 36 = opp/hyp

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29.

✔️Sin 70 = opp/hyp

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2 years ago
Any help please? For extra credit
Law Incorporation [45]

Answer:

see explanation

Step-by-step explanation:

(a)

A recursive formula allows any term in the sequence to be found by adding the common difference d to the previous term.

Here d = - 4 , then recursive formula is

a_{n} = a_{n-1} - 4 with a₁ = 2

(b)

The explicit formula for an arithmetic sequence is

a_{n} = a₁ + (n - 1)d

where a₁ is the first term and d the common difference

Here a₁ = 2 and d = - 4, thus

a_{n} = 2 - 4(n - 1) = 2 - 4n + 4 = 6 - 4n ← explicit formula

(c)

Using the recursive formula

a₁ = 2

a₂ = 2 - 4 = - 2

a₃ = - 2 - 4 = - 6

Using the explicit formula

a₅ = 6 - 4(5) = 6 - 20 = - 14

a₁₀ = 6 - 4(10) = 6 - 40 = - 34

a₁₀₀ = 6 - 4(100) = 6 - 400 = - 394

4 0
2 years ago
leos total bill at the blue lobster ame to $45.90. He wanted to leave a 20% tip what would the total cost with the be?
elena-s [515]
To find the total amount Leo should give, simply find the 20% of his bill then add it.

Total cost = $45.90 + ($45.90 × 0.20)
Total cost = $45.90 + $9.18
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Therefore, Leo should give $55.08 in total to leave a 20% tip.
7 0
3 years ago
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