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mamaluj [8]
3 years ago
12

Graph each of the equations and then determine which one represents the rank catcher that is elevated

Mathematics
1 answer:
Tanya [424]3 years ago
5 0
We have two functions that are Parabolas. A parabola is a type of quadratic function which is a special type of “U”-shaped curve called. So let's solve this problem for the first parabola and then for the second one.

1. Graph of the first equation

We have that:

y=x^2-2x+3

So if we graph this equation, the parabola that matches it is shown in Figure 1.

1.1 Direction of Parabola

In general, a parabola or quadratic function is given by the following way:

y=ax^2+bx+c \\ \\ where \ "a" \ is \ called \ the \ leading \ coefficient

Given that our leading coefficient is positive, then the direction of the parabola is upward, that is, it opens upward.

1.2 Location of vertex with respect to the x-axis

The vertex a parabola can be found as follows:

(-\frac{b}{2a},f(-\frac{b}{2a}))

But: \\ \\ a=1 \\ b=-2 \\ c=3 \\ \\ Accordingly: \\ \\ -\frac{b}{2a}=-\frac{(-2)}{2(1)}=1 \\ \\ f(1)=1^2-2(1)+3=2 \\ \\ So \ the \ vertex \ is: \\ \\ V(1,2)

So the vertex is located two units above the x-axis.

<span>1.3 Determine if the graph depicts the rain gauge
</span>
A rain gauge is an instrument used by meteorologists and hydrologists to gather and measure the amount of liquid precipitation<span> over a set period of time.
</span>
From Figure 4 we can affirm that this is the parabola that resembles a rain gauge elevated from the ground. 

1.4 Why or why not?

It basically the question asks for the parabola that has a vertex well above the x-axis. From Figure 4, you can see that the elevated parabola is in fact:

y=x^2-2x+3

2. Graph of the second equation

We have that:

y=x^2+4x+4

So if we graph this equation, the parabola that matches it is shown in Figure 2.

2.1 Direction of Parabola

As in the previous problem, given that our leading coefficient is positive, then the direction of the parabola is also upward, that is, it opens upward.

2.2 Location of vertex with respect to the x-axis

The vertex of a parabola can be found as follows:

(-\frac{b}{2a},f(-\frac{b}{2a}))

In \ this \ case: \\ \\ a=1 \\ b=4 \\ c=3 \\ \\ Accordingly: \\ \\ -\frac{b}{2a}=-\frac{4}{2(1)}=-2 \\ \\ f(-2)=(-2)^2+4(-2)+4=0 \\ \\ So \ the \ vertex \ is: \\ \\ V(-2,0)

So the vertex lies on the x-axis.

2.3 Determine if the graph depicts the rain gauge

This parabola does not resembles a rain gauge elevated from the ground.

2.4 Why or why not?

As you can see the parabola touches the x-axis. If the x-axis represents the ground, then the rain gauge is touching it, that is, it is not elevated.

3. Graph of the third equation

We have that:

y=3x^2+21x+30

So if we graph this equation, the parabola that matches it is shown in Figure 5.

3.1 Direction of Parabola

As in the previous parabolas, given that our leading coefficient is positive, then the direction of the parabola is also upward, that is, it opens upward.

3.2 Location of vertex with respect to the x-axis

In \ this \ case: \\ \\ a=3 \\ b=21 \\ c=30 \\ \\ Accordingly: \\ \\ -\frac{b}{2a}=-\frac{21}{2(3)}=-\frac{7}{2} \\ \\ f(-\frac{7}{2})=3(-\frac{7}{2})^2+21(-\frac{7}{2})+30=-\frac{27}{4} \\ \\ So \ the \ vertex \ is: \\ \\ V(-\frac{7}{2},-\frac{27}{4})

So the vertex is shifted \frac{27}{4} units downward the x-axis.

3.3 Determine if the graph depicts the rain gauge

This parabola does not resembles a rain gauge elevated from the ground.

3.4 Why or why not?

The vertex of this parabola lies on the negative y-axis. So it is not elevated from the ground.

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Answer: 168

Step-by-step explanation: When your faced with a longer problem that involves some multiplication of positives and negatives, make sure you work the problem carefully from left to right.

So the first thing we want to do here is to

multiply -4 by 6 and that gives us -24.

Now bring down the (-7) and we have -24 (-7) which is 168.

So our answer is 168.

8 0
3 years ago
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4) Write the equation of the line in
Pani-rosa [81]

Step-by-step explanation:

(x1,y1) = (-2,5)

(x2,y2) = (5,-2)

(y - y1)/(y2 - y1) = (x - x1)/(x2 - x1)

(y - 5)/(-2 - 5) = (x + 2)/(5 + 2)

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3 years ago
Choose the best answer​
Dafna1 [17]

\quad \huge \quad \quad \boxed{ \tt \:Answer }

\qquad \tt \rightarrow \:-\dfrac{1}{\sqrt{3-2x}}

____________________________________

\large \tt Solution  \: :

We newd to find the derivative of given function :

\qquad \tt \rightarrow \: y =  \sqrt{3 - 2x}

\qquad \tt \rightarrow \: y = (3 - 2x) {}^{ \frac{1}{2} }

\qquad \displaystyle \tt \rightarrow \:   \frac{dy}{dx}  =  \frac{d}{dx} (3 - 2x) {}^{ \frac{1}{2} }

\qquad \displaystyle \tt \rightarrow \:   \frac{dy}{dx}  =   \frac{1}{2}  \sdot(3 - 2x) {}^{ -  \frac{1}{2} }  \sdot( - 2)

\qquad \displaystyle \tt \rightarrow \:   \frac{dy}{dx}  =   \frac{1}{ \cancel2}    \sdot\frac{1}{(3 - 2x) {}^{  \frac{1}{2} }  }\sdot( -  \cancel2)

\qquad \displaystyle \tt \rightarrow \:   \frac{dy}{dx}  =      \frac{ - 1}{ \sqrt{ (3 - 2x) {}^{   }}  }

Correct option : B

Answered by : ❝ AǫᴜᴀWɪᴢ ❞

3 0
1 year ago
HELP ME PLS ! <br> BRAINLISTTT
artcher [175]

Answer:

I think A

Step-by-step explanation:

its quirky and Im not even in this math yet

3 0
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faltersainse [42]
Yes it is correct because if you multiply 3 by the value of x(7) and add 4 your answer is 25.
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