Factor 2x+4 (Please and Thanks)
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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:
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:
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:
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:
2. Graph of the second equation
We have that:
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:
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:
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
So the vertex is shifted
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.
1. Graph of the first equation
We have that:
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:
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:
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:
2. Graph of the second equation
We have that:
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:
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:
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
So the vertex is shifted
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.
The rigorous way to do this would be to compute a few integrals, but less work is usually better. Each of these probabilities correspond to the areas of rectangles. Each rectangle will have a height of 1, and the probability of interest will tell you everything you need to know about their lengths.
Alternatively, you can use the fact that
to get the same result.
Alternatively, you can use the fact that