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3 years ago

What is the equation in vertex form of the quadratic function with a vertex at (-1, -4) that goes through (1, 8)?

Mathematics

1 answer:

cestrela7 [59]3 years ago

5 0

Answer:

y = 3(x+1)^2 - 4

Step-by-step explanation:The general form of the equation of a quadratic function whose vertex is (h,k) and whose leading coefficient is a is:

y - k = a(x-h)^2, or

y = a(x-h)^2 - k

Substituting the coefficients of the vertex (-1, -4), we get:

y = a(x + 1)^2 - 4

Substituting the coordinates of the given point, (1,8), we get:

8 = a(1+1)^2 - 4, which simplifies to:

8 = a(2)^2 - 4, or

8 = 4a - 4. Then 4a = 12, and a = 3.

Thus, the desired equation is y = 3(x+1)^2 - 4 (answer j).

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Jaina and Tomas compare their compound interest accounts to see how much they will have in the accounts after three years. They

MariettaO [177]

The question is incomplete. The complete question is :

Jaina and Tomas compare their compound interest accounts to see how much they will have in the accounts after three years. They substitute their values shown below into the compound interest formula. Compound Interest Accounts Name Principal Interest Rate Number of Years Compounded Jaina $300 7% 3 Once a year Tomas $400 4% 3 Once a year. Which pair of equations would correctly calculate their compound interests?

Solution :

It is given that Jaina and Tomas wants to open an account by depositing a principal amount for a period of 3 years and wanted to calculate the amount they will have using the compound interest formula.

So for Jiana :

Principal, P = $300

Rate of interest, r = 7%

Time, t = 3

Compounded yearly

Therefore, using compound interest formula, we get

$A=P\left(1+\frac{r}{100}\right)^{t}$

$=300\left(1+\frac{7}{100}\right)^{3}$

$=300(1+0.07)^3$

Now for Tomas :

Principal, P = $400

Rate of interest, r = 4%

Time, t = 3

Compounded yearly

Therefore, using compound interest formula, we get

$A=P\left(1+\frac{r}{100}\right)^{t}$

$=400\left(1+\frac{4}{100}\right)^{3}$

$=400(1+0.04)^3$

Therefore, the pair of equations that would correctly calculate the compound interests for Jaina is $A=300(1+0.07)^3$ .

And the pair of equations that would correctly calculate the compound interests for Tomas is $A=400(1+0.04)^3$ .

8 0

2 years ago

Read 2 more answers

Through:(3,-1),slope=-1

Wewaii [24]

Answer:

y = -x + 2

Step-by-step explanation:

Use the point-slope formula y - k = m(x -h):

y - [-1] = -1(x - 3), or

y + 1 = -x + 3, or

y = -x + 2

5 0

3 years ago

8(3a+5)???? please help!!!!!! ASAP!!!!

r-ruslan [8.4K]

I'm assuming your teacher wants you to distribute. If so, then you multiply the outer term 8 by each term inside (3a and 5). After that you add.

8 times 3a = 24a

8 times 5 = 40

So 8(3a+5) becomes 24a+40

We do not combine 24a and 40 as they are not like terms. So we leave 24a+40 as it is.

3 0

2 years ago

Read 2 more answers

Lexi Susie and Ryan are playing on online word game Royals score 100034 points Lexi scores 9348 fewer points t

11Alexandr11 [23.1K]

100,435 hope this helps you

7 0

3 years ago

Y is directly proportional to square root of x If y=56 when x=49 find, y when x=81

STALIN [3.7K]

$\qquad \qquad \textit{direct proportional variation} \\\\ \textit{\underline{y} varies directly with \underline{x}}\qquad \qquad \stackrel{\textit{constant of variation}}{y=\stackrel{\downarrow }{k}x~\hfill } \\\\ \textit{\underline{x} varies directly with }\underline{z^5}\qquad \qquad \stackrel{\textit{constant of variation}}{x=\stackrel{\downarrow }{k}z^5~\hfill } \\\\[-0.35em] \rule{34em}{0.25pt}$

$\stackrel{\begin{array}{llll} \textit{"y" directly}\\ \textit{proportional to }\sqrt{x} \end{array}}{y = k\sqrt{x}}\qquad \textit{we know that} \begin{cases} y = 56\\ x = 49 \end{cases}\implies 56=k\sqrt{49} \\\\\\ 56=7k\implies \cfrac{56}{7}=k\implies 8=k~\hfill \boxed{y=8\sqrt{x}} \\\\\\ \textit{when x = 81, what is "y"?}\hfill y=8\sqrt{81}\implies y=8(9)\implies y=72$

7 0

2 years ago