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Alika [10]
3 years ago
10

The function f(x) = x2 + 6x + 3 is transformed such that g(x) = f(x − 2). Find the vertex of g(x).

Mathematics
1 answer:
garri49 [273]3 years ago
6 0

Answer:

(-1,-6)

Step-by-step explanation:

f(x)=x^2+6x+3

g(x)=f(x-2)

g(x)=(x-2)^2+6(x-2)+3  (Replaced x in f with (x-2))

g(x)=x^2-4x+4+6x-12+3 (Used (x+b)^2=x^2+2bx+b^2 and distributive property)

g(x)=x^2-4x+6x+4-12+3 (Gathered like terms)

g(x)=x^2+2x-5  (Simplified)

The vertex of a parabola occurs at (\frac{-b}{2a},g(\frac{-b}{2a}).

Let's find \frac{-b}{2a} first.

\frac{-2}{2(1)}=-1

Now we can obtain g(\frac{-b}{2a}) which is g(-1) in this case:

g(x)=x^2+2x-5

g(-1)=(-1)^2+2(-1)-5

g(-1)=1-2-5

g(-1)=-1-5

g(-1)=-6.

The vertex is (-1,-6).

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Answer:

When Aria sold her house after eleven years it worth was <u>$95,300</u>.

Step-by-step explanation:

Given:

Aria paid $75,000 for her house. Its property value increased by 2.2% per year.

Now, to find the worth of Aria house when sold after eleven years.

Let the amount of house after eleven years be x.

Amount Aria paid for her house (A) = $75,000.

Rate of property increased per year (r) = 2.2%.

Time (t) = 11 years.

Now, to get the amount of house after eleven years we put formula:

x=A\times (1+\frac{r}{100})^{11}

x=75000\times (1+\frac{2.2}{100})^{11}

x=75000\times (1+0.022)^{11}

x=75000\times (1.022)^{11}

x=75000\times 1.2704

x=95280.

<em>The amount of house after eleven years to the nearest hundred dollars is $95,300.</em>

Therefore, when Aria sold her house after eleven years it worth was $95,300.

3 0
3 years ago
There are as many girls as there are boys in a class. 8 girls went for a dance competition. now there are twice as many boys as
Rashid [163]
Let the number of girls be x and the number of boys be y

The number of boys is the same as the number of girls.
x = y 
The number of boys is twice the number of girls when 8 girls left.
2(x - 8) = y


x = y ---------------- (1)
2(x - 8) = y -------- (2)

Sub (1) into (2)

2(y - 8) = y
2y - 16 = y
2y - y = 16
y = 16
There were 16 boys and 16 girls initially.

16 + 16 = 32 
There were a total of 32 students in the class initially. 



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daser333 [38]

Answer:

V≈113.1

Step-by-step explanation:

V=πr2h

3=π·32·12

3≈113.09734

5 0
3 years ago
On a piece of paper, graph this system of inequalities. Then determine which
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Answer:

B.Reigion D

Step-by-step explanation:

6 0
3 years ago
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(PLZ SOLVE ASAP I DONT UNDERSTAND THIS) <br> 4x − 1 ≥ x + 7 and x + 7 &gt; 2 − 4x
Vedmedyk [2.9K]

Answer:

3 + ? = 7, 3 + n = 7, 3 + x = 1

so 1 is the answer for the first question

Step-by-step explanation:

6 0
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