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Hitman42 [59]
3 years ago
10

Please help? (03.04) What are the coordinates of the vertex for f(x) = x^2 + 4x + 10?

Mathematics
1 answer:
GREYUIT [131]3 years ago
8 0

Answer:

(-2, 6)

Step-by-step explanation:

f(x) = x² + 4x + 10

f(x) = x² + 4x + 4 + 6

f(x) = (x + 2)² + 6

The vertex is at (-2, 6).

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HELLOOOO HELP PLEASE
MA_775_DIABLO [31]

Answer:

2*log(x)+log(y)

Step-by-step explanation:

So, there are two logarithmic identities you're going to need to know.

<em>Logarithm of a power</em>:

   log_ba^c=c*log_ba

   So to provide a quick proof and intuition as to why this works, let's consider the following logarithm: log_ba=x\implies b^x=a

   Now if we raise both sides to the power of c, we get the following equation: (b^x)^c=a^c

   Using the exponential identity: (x^a)^c=x^{a*c}

    We get the equation: b^{xc}=a^c

    If we convert this back into logarithmic form we get: log_ba^c=x*c

    Since x was the basic logarithm we started with, we substitute it back in, to get the equation: log_ba^c=c*log_ba

Now the second logarithmic property you need to know is

<em>The Logarithm of a Product</em>:

    log_b{ac}=log_ba+log_bc

    Now for a quick proof, let's just say: x=log_ba\text{ and }y=log_bc

    Now rewriting them both in exponential form, we get the equations:

    b^x=a\\b^y=c

    We can multiply a * c, and since b^x = a, and b^y = c, we can substitute that in for a * c, to get the following equation:

    b^x*b^y=a*c

   Using the exponential identity: x^{a}*x^b=x^{a+b}, we can rewrite the equation as:

 

   b^{x+y}=ac

   taking the logarithm of both sides, we get:

   log_bac=x+y

   Since x and y are just the logarithms we started with, we can substitute them back in to get: log_bac=log_ba+log_bc

Now let's use these identities to rewrite the equation you gave

log(x^2y)

As you can see, this is a log of products, so we can separate it into two logarithms (with the same base)

log(x^2)+log(y)

Now using the logarithm of a power to rewrite the log(x^2) we get:

2*log(x)+log(y)

3 0
2 years ago
A rectangle has base length
vekshin1
I believe that the answer is 22x
3 0
3 years ago
942 ÷ 7 = ? A. 134 R4 B. 136 C. 134 R2 D. 133 R1
zimovet [89]

Answer:


Step-by-step explanation:

134

5 0
3 years ago
Read 2 more answers
Can someone help me part 2
Otrada [13]

Step-by-step explanation:

y = ¼x + 2

m1 = ¼

m of line perpendicular = m2

the formula is : m1×m2 = -1

=> m2 = -1 ÷ m1

= -1 ÷ ¼ = -4

so, the equation is :

y = -4x - 7 (option A)

3 0
3 years ago
Pls answer quickly
Grace [21]

Answer:

B. 10

Step-by-step explanation:

Look at the chart.

Find how many members are 50-60 inches tall. (6)

Find how many members are 61-70 inches tall. (4)

Add each member count up. (10)

4 0
2 years ago
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