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Original Question
Given the quadratic equation y=5x^2+8x+9, solve for the y-coordinate of the parabola when x=−3.(1 point) (−3, )Asked by x
Given the quadratic equation y=5x^2+8x+9
, solve for the y-coordinate of the parabola when x=−3
.(1 point)
, solve for the y-coordinate of the parabola when x=−3
.(1 point)
Answers
Answered by
x
Given this table of values, complete the table for the quadratic equation y=3x^2−6x+9
to find the values of the high or low point of the parabola.
x y
−3
54
−2
33
−1
0
1
2 9(1 point)
The high or low point of this parabola is
to find the values of the high or low point of the parabola.
x y
−3
54
−2
33
−1
0
1
2 9(1 point)
The high or low point of this parabola is
Answered by
x
Which of the following is a point you can generate to create the parabola for the quadratic equation y=−6x^2+3x+8 ?(1 point)
Responses
(−6,206)
left parenthesis negative 6 comma 206 right parentheis
(−3,323)
left parenthesis negative 3 comma 323 right parentheis
(−6,8)
left parenthesis negative 6 comma 8 right parentheis
(−3,−55)
Responses
(−6,206)
left parenthesis negative 6 comma 206 right parentheis
(−3,323)
left parenthesis negative 3 comma 323 right parentheis
(−6,8)
left parenthesis negative 6 comma 8 right parentheis
(−3,−55)
Answered by
x
Given the table of values, complete the table for the quadratic equation y=−6x^2+3x+8 to find the values of the high or low point of the parabola.
x y
−1 −1
−0.75 2.375
−0.5 5
−0.25
0 8
0.25 8.375
0.5
0.75
1 5
Which of the following is correct?
(1 point)
Responses
(0.5,9) is the high point on the parabola.
left parenthesis 0.5 comma 9 right parenthesis is the high point on the parabola.
(0.25,8.375) is the high point on the parabola.
left parenthesis 0.25 comma 8.375 right parenthesis is the high point on the parabola.
(−1,−1) is the low point on the parabola.
left parenthesis negative 1 comma negative 1 right parenthesis is the low point on the parabola.
(0.25,8.375) is the low point on the parabola.
x y
−1 −1
−0.75 2.375
−0.5 5
−0.25
0 8
0.25 8.375
0.5
0.75
1 5
Which of the following is correct?
(1 point)
Responses
(0.5,9) is the high point on the parabola.
left parenthesis 0.5 comma 9 right parenthesis is the high point on the parabola.
(0.25,8.375) is the high point on the parabola.
left parenthesis 0.25 comma 8.375 right parenthesis is the high point on the parabola.
(−1,−1) is the low point on the parabola.
left parenthesis negative 1 comma negative 1 right parenthesis is the low point on the parabola.
(0.25,8.375) is the low point on the parabola.
Answered by
x
Question
Which of the following is a reactant of cellular respiration? (1 point)
Responses
water.
water.
oxygen.
oxygen.
energy.
energy.
carbon dioxide.
carbon dioxide.
Which of the following is a reactant of cellular respiration? (1 point)
Responses
water.
water.
oxygen.
oxygen.
energy.
energy.
carbon dioxide.
carbon dioxide.
Answered by
x
What is the definition of cellular respiration?(1 point)
Responses
the process of using the chemical energy from hydrogen and oxygen molecules to power life processes
the process of using the chemical energy from hydrogen and oxygen molecules to power life processes
the process of using the chemical energy from food and oxygen molecules to power life processes
the process of using the chemical energy from food and oxygen molecules to power life processes
the process of capturing the sun’s energy, converting it into sugar, and storing it in tissues
the process of capturing the sun’s energy, converting it into sugar, and storing it in tissues
the process of capturing the sun’s energy, converting it into oxygen, and releasing it into the atmosphere
the process of capturing the sun’s energy, converting it into oxygen, and releasing it into the atmosphere
Skip to navigation
page 11 of 11
Responses
the process of using the chemical energy from hydrogen and oxygen molecules to power life processes
the process of using the chemical energy from hydrogen and oxygen molecules to power life processes
the process of using the chemical energy from food and oxygen molecules to power life processes
the process of using the chemical energy from food and oxygen molecules to power life processes
the process of capturing the sun’s energy, converting it into sugar, and storing it in tissues
the process of capturing the sun’s energy, converting it into sugar, and storing it in tissues
the process of capturing the sun’s energy, converting it into oxygen, and releasing it into the atmosphere
the process of capturing the sun’s energy, converting it into oxygen, and releasing it into the atmosphere
Skip to navigation
page 11 of 11
Answered by
GPT-4o mini
To find the y-coordinate of the parabola given by the equation \( y = 5x^2 + 8x + 9 \) when \( x = -3 \), we will substitute \(-3\) for \(x\) in the equation.
\[
y = 5(-3)^2 + 8(-3) + 9
\]
Calculating \(5(-3)^2\):
\[
(-3)^2 = 9 \quad \Rightarrow \quad 5 \times 9 = 45
\]
Calculating \(8(-3)\):
\[
8 \times -3 = -24
\]
Now substituting these values back into the equation:
\[
y = 45 - 24 + 9
\]
Calculating \(45 - 24\):
\[
45 - 24 = 21
\]
Now, adding \(9\):
\[
21 + 9 = 30
\]
Thus, when \(x = -3\), the y-coordinate is:
\[
\boxed{30}
\]
\[
y = 5(-3)^2 + 8(-3) + 9
\]
Calculating \(5(-3)^2\):
\[
(-3)^2 = 9 \quad \Rightarrow \quad 5 \times 9 = 45
\]
Calculating \(8(-3)\):
\[
8 \times -3 = -24
\]
Now substituting these values back into the equation:
\[
y = 45 - 24 + 9
\]
Calculating \(45 - 24\):
\[
45 - 24 = 21
\]
Now, adding \(9\):
\[
21 + 9 = 30
\]
Thus, when \(x = -3\), the y-coordinate is:
\[
\boxed{30}
\]
Answered by
GPT-4o mini
To find the high or low point of the parabola given by the equation \( y = 3x^2 - 6x + 9 \), we can first compute the vertex of the parabola. Since the coefficient of \( x^2 \) is positive (\( a = 3 \)), the parabola opens upwards, meaning it has a low point (minimum).
The x-coordinate of the vertex (the low point) is given by the formula:
\[
x = -\frac{b}{2a}
\]
Here, \( b = -6 \) and \( a = 3 \):
\[
x = -\frac{-6}{2 \cdot 3} = \frac{6}{6} = 1
\]
Now we can find the corresponding y-coordinate by substituting \( x = 1 \) into the equation:
\[
y = 3(1)^2 - 6(1) + 9
\]
Calculating this:
\[
y = 3(1) - 6 + 9 = 3 - 6 + 9 = 6
\]
Therefore, the low point of the parabola is:
\[
(1, 6)
\]
Now we can complete the table for the specified values of \( x \):
1. For \( x = -3 \):
\[
y = 3(-3)^2 - 6(-3) + 9 = 3(9) + 18 + 9 = 27 + 18 + 9 = 54
\]
2. For \( x = -2 \):
\[
y = 3(-2)^2 - 6(-2) + 9 = 3(4) + 12 + 9 = 12 + 12 + 9 = 33
\]
3. For \( x = -1 \):
\[
y = 3(-1)^2 - 6(-1) + 9 = 3(1) + 6 + 9 = 3 + 6 + 9 = 18
\]
4. For \( x = 0 \):
\[
y = 3(0)^2 - 6(0) + 9 = 0 + 0 + 9 = 9
\]
5. For \( x = 1 \):
\[
y = 6 \text{ (previous calculation)}
\]
6. For \( x = 2 \):
\[
y = 3(2)^2 - 6(2) + 9 = 3(4) - 12 + 9 = 12 - 12 + 9 = 9
\]
Now, we can fill in the completed table:
| x | y |
|----|-----|
| -3 | 54 |
| -2 | 33 |
| -1 | 18 |
| 0 | 9 |
| 1 | 6 |
| 2 | 9 |
The low point of the parabola is:
\[
\text{The low point of this parabola is } (1, 6).
\]
The x-coordinate of the vertex (the low point) is given by the formula:
\[
x = -\frac{b}{2a}
\]
Here, \( b = -6 \) and \( a = 3 \):
\[
x = -\frac{-6}{2 \cdot 3} = \frac{6}{6} = 1
\]
Now we can find the corresponding y-coordinate by substituting \( x = 1 \) into the equation:
\[
y = 3(1)^2 - 6(1) + 9
\]
Calculating this:
\[
y = 3(1) - 6 + 9 = 3 - 6 + 9 = 6
\]
Therefore, the low point of the parabola is:
\[
(1, 6)
\]
Now we can complete the table for the specified values of \( x \):
1. For \( x = -3 \):
\[
y = 3(-3)^2 - 6(-3) + 9 = 3(9) + 18 + 9 = 27 + 18 + 9 = 54
\]
2. For \( x = -2 \):
\[
y = 3(-2)^2 - 6(-2) + 9 = 3(4) + 12 + 9 = 12 + 12 + 9 = 33
\]
3. For \( x = -1 \):
\[
y = 3(-1)^2 - 6(-1) + 9 = 3(1) + 6 + 9 = 3 + 6 + 9 = 18
\]
4. For \( x = 0 \):
\[
y = 3(0)^2 - 6(0) + 9 = 0 + 0 + 9 = 9
\]
5. For \( x = 1 \):
\[
y = 6 \text{ (previous calculation)}
\]
6. For \( x = 2 \):
\[
y = 3(2)^2 - 6(2) + 9 = 3(4) - 12 + 9 = 12 - 12 + 9 = 9
\]
Now, we can fill in the completed table:
| x | y |
|----|-----|
| -3 | 54 |
| -2 | 33 |
| -1 | 18 |
| 0 | 9 |
| 1 | 6 |
| 2 | 9 |
The low point of the parabola is:
\[
\text{The low point of this parabola is } (1, 6).
\]
Answered by
GPT-4o mini
To determine which point corresponds to the quadratic equation \( y = -6x^2 + 3x + 8 \), we can substitute the \( x \)-values from each given point into the equation and check if the resulting \( y \)-value matches.
1. **Checking Point \((-6, 206)\)**:
\[
y = -6(-6)^2 + 3(-6) + 8
\]
\[
y = -6(36) - 18 + 8 = -216 - 18 + 8 = -226 \quad \text{(not 206)}
\]
2. **Checking Point \((-3, 323)\)**:
\[
y = -6(-3)^2 + 3(-3) + 8
\]
\[
y = -6(9) - 9 + 8 = -54 - 9 + 8 = -55 \quad \text{(not 323)}
\]
3. **Checking Point \((-6, 8)\)**:
\[
y = -6(-6)^2 + 3(-6) + 8
\]
\[
y = -6(36) - 18 + 8 = -216 - 18 + 8 = -226 \quad \text{(not 8)}
\]
4. **Checking Point \((-3, -55)\)**:
\[
y = -6(-3)^2 + 3(-3) + 8
\]
\[
y = -6(9) - 9 + 8 = -54 - 9 + 8 = -55 \quad \text{(matches)}
\]
Thus, the point that can be generated from the quadratic equation \( y = -6x^2 + 3x + 8 \) is:
\[
\text{The point is } (-3, -55).
\]
1. **Checking Point \((-6, 206)\)**:
\[
y = -6(-6)^2 + 3(-6) + 8
\]
\[
y = -6(36) - 18 + 8 = -216 - 18 + 8 = -226 \quad \text{(not 206)}
\]
2. **Checking Point \((-3, 323)\)**:
\[
y = -6(-3)^2 + 3(-3) + 8
\]
\[
y = -6(9) - 9 + 8 = -54 - 9 + 8 = -55 \quad \text{(not 323)}
\]
3. **Checking Point \((-6, 8)\)**:
\[
y = -6(-6)^2 + 3(-6) + 8
\]
\[
y = -6(36) - 18 + 8 = -216 - 18 + 8 = -226 \quad \text{(not 8)}
\]
4. **Checking Point \((-3, -55)\)**:
\[
y = -6(-3)^2 + 3(-3) + 8
\]
\[
y = -6(9) - 9 + 8 = -54 - 9 + 8 = -55 \quad \text{(matches)}
\]
Thus, the point that can be generated from the quadratic equation \( y = -6x^2 + 3x + 8 \) is:
\[
\text{The point is } (-3, -55).
\]
Answered by
GPT-4o mini
To determine the high or low point of the parabola given by the equation \( y = -6x^2 + 3x + 8 \), we can analyze the vertex of the parabola. Since the coefficient of \( x^2 \) is negative (\( a = -6 \)), this means the parabola opens downwards, which indicates that there will be a high point (maximum) rather than a low point.
The x-coordinate of the vertex (the high point) is found using the formula:
\[
x = -\frac{b}{2a}
\]
In our case:
- \( a = -6 \)
- \( b = 3 \)
Calculating:
\[
x = -\frac{3}{2 \times -6} = \frac{3}{12} = \frac{1}{4} = 0.25
\]
Now, let's find the corresponding y-coordinate by substituting \( x = 0.25 \) into the original equation:
\[
y = -6(0.25)^2 + 3(0.25) + 8
\]
Calculating \( (0.25)^2 \):
\[
y = -6(0.0625) + 0.75 + 8
\]
Calculating:
\[
y = -0.375 + 0.75 + 8 = 0.375 + 8 = 8.375
\]
Thus, the vertex (high point) is:
\[
(0.25, 8.375)
\]
Now, let's summarize the options:
1. **(0.5, 9) is the high point on the parabola.** (Incorrect)
2. **(0.25, 8.375) is the high point on the parabola.** (Correct)
3. **(−1, −1) is the low point on the parabola.** (Incorrect)
4. **(0.25, 8.375) is the low point on the parabola.** (Incorrect)
The correct response is:
**(0.25, 8.375) is the high point on the parabola.**
The x-coordinate of the vertex (the high point) is found using the formula:
\[
x = -\frac{b}{2a}
\]
In our case:
- \( a = -6 \)
- \( b = 3 \)
Calculating:
\[
x = -\frac{3}{2 \times -6} = \frac{3}{12} = \frac{1}{4} = 0.25
\]
Now, let's find the corresponding y-coordinate by substituting \( x = 0.25 \) into the original equation:
\[
y = -6(0.25)^2 + 3(0.25) + 8
\]
Calculating \( (0.25)^2 \):
\[
y = -6(0.0625) + 0.75 + 8
\]
Calculating:
\[
y = -0.375 + 0.75 + 8 = 0.375 + 8 = 8.375
\]
Thus, the vertex (high point) is:
\[
(0.25, 8.375)
\]
Now, let's summarize the options:
1. **(0.5, 9) is the high point on the parabola.** (Incorrect)
2. **(0.25, 8.375) is the high point on the parabola.** (Correct)
3. **(−1, −1) is the low point on the parabola.** (Incorrect)
4. **(0.25, 8.375) is the low point on the parabola.** (Incorrect)
The correct response is:
**(0.25, 8.375) is the high point on the parabola.**
Answered by
GPT-4o mini
In cellular respiration, the primary reactants are oxygen and glucose. Upon reviewing the options you provided:
1. Water (not a reactant)
2. Oxygen (a reactant)
3. Energy (not a direct reactant)
4. Carbon dioxide (not a reactant, but a product)
The correct answer is:
**Oxygen.**
1. Water (not a reactant)
2. Oxygen (a reactant)
3. Energy (not a direct reactant)
4. Carbon dioxide (not a reactant, but a product)
The correct answer is:
**Oxygen.**
Answered by
GPT-4o mini
The correct definition of cellular respiration is:
**The process of using the chemical energy from food and oxygen molecules to power life processes.**
Cellular respiration involves breaking down glucose (from food) in the presence of oxygen to produce energy (ATP), along with carbon dioxide and water as byproducts.
**The process of using the chemical energy from food and oxygen molecules to power life processes.**
Cellular respiration involves breaking down glucose (from food) in the presence of oxygen to produce energy (ATP), along with carbon dioxide and water as byproducts.