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Leya [2.2K]
3 years ago
14

What is f(x) = 7x2 + 42x written in vertex form?

Mathematics
2 answers:
amid [387]3 years ago
7 0

Answer:

\boxed{\boxed{y = 7(x+3)^2-63}}

Step-by-step explanation:

The general vertex form of parabola is,

y=a(x-h)+k

where,

(h, k) is the vertex of the parabola.

The given function is,

\Rightarrow f(x) = 7x^2 + 42x

\Rightarrow y = 7x^2 + 42x

\Rightarrow y = 7(x^2 + 6x)

\Rightarrow y = 7(x^2 + 2\cdot x\cdot 3)

\Rightarrow y = 7(x^2 + 2\cdot x\cdot 3+3^3-3^2)

\Rightarrow y = 7(x^2 + 2\cdot x\cdot 3+3^3)-7\cdot 3^2

\Rightarrow y = 7(x+3)^2-7\cdot 9

\Rightarrow y = 7(x+3)^2-63

This is vertex form the given function.

max2010maxim [7]3 years ago
6 0
Hello,

y=7x²+42x
==>y=7(x²+2*3*x+9)-63
==>y=7(x+3)²-63


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Felipe borrowed $8000 at a rate of 16.5%, compounded monthly. Assuming he makes no payments, how much will he owe after 7 years?
Gelneren [198K]

Answer:

$25,193.17

Explanation:

Given:

• Principal Felipe borrowed, P=$8000

,

• Annual Interest Rate, r=16.5%=0.165

,

• Compounding Period, k=12 (Monthly)

,

• Time, t=7 years

We want to determine how much he will owe after 7 years.

In order to carry out this calculation, use the compound interest formula below:

A(t)=P\mleft(1+\frac{r}{k}\mright)^{tk}

Substitute the values defined above:

A(t)=8000\mleft(1+\frac{0.165}{12}\mright)^{12\times7}

Finally, simplify and round to the nearest cent.

\begin{gathered} A(t)=8000(1+0.01375)^{84} \\ =8000(1.01375)^{84} \\ =\$25,193.17 \end{gathered}

After 7 years, Felipe will owe $25,193.17.

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Step-by-step explanation:

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