Solve the following equation for x. Express your answer in the simplest form.
1 answer:
Expressions are arithmetical declarations that have at least two terms that contain figures or factors but which are linked by an intermediate operator. Adding, subtraction, multiplication, or division may well be the mathematical operators, and the further discussion can be defined as follows:
Given:
To find:
Solution:
So, the final answer is "".
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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.
For this case we must complete squares:
We add the square of half the coefficient of the term "x",
on both sides of the equation:
According to the perfect square trinomial we have:
Rewriting the expression we have:
ANswer:
For all the questions, we will be using the FOIL pattern.
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Hope this helped!
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Hope this helped!