Question
Can you help with the parabola it opens downward, at the top right side the number is (-1.25, 15.125) going on down is (0,12) at the bottom is (1.5,0) then on the left side at the bottom inside the parabola is (-4,0) can you tell me where it increase, decreases, positive, negative, and the axis of symmetry,
Answers
Answer
Can you give me the numbers where it decreases and increases and which are positive and negative and the axis of symmetry please
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So are you saying any numbers on the left side will be increasing and the numbers on the right are decreasing is that right
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I'm sorry for asking so many questions I believe the vertex is at the points (-1.25, 15.125) at the very top the maximum point I think, is that also the axis of symmetry
Answered by
GPT 3.5
It looks like the parabola you're describing has the equation of the form y = ax^2 + bx + c, where a is negative (meaning the parabola opens downward).
From the given points, we can find the coefficients of the parabola:
1. The point at the top right (-1.25, 15.125) can be used to find a. Plugging in these values into the equation gives: 15.125 = a(-1.25)^2 - b(1.25) + c
2. The point at (0, 12) gives: 12 = a(0)^2 + b(0) + c
3. The point at the bottom (1.5, 0) gives: 0 = a(1.5)^2 + b(1.5) + c
4. The point (-4, 0) gives: 0 = a(-4)^2 + b(-4) + c
By solving these equations simultaneously, you can find the values of a, b, and c. Once you have these values, you can analyze the parabola:
- Increase/Decrease: The parabola will be increasing to the left of the axis of symmetry, and decreasing to the right of the axis of symmetry.
- Positive/Negative: The parabola will be positive above the axis of symmetry (vertex), and negative below the axis of symmetry.
- Axis of Symmetry: The axis of symmetry can be found by the formula x = -b / (2a).
By plugging in the values of a and b, you can calculate the exact location of the vertex and the axis of symmetry.
From the given points, we can find the coefficients of the parabola:
1. The point at the top right (-1.25, 15.125) can be used to find a. Plugging in these values into the equation gives: 15.125 = a(-1.25)^2 - b(1.25) + c
2. The point at (0, 12) gives: 12 = a(0)^2 + b(0) + c
3. The point at the bottom (1.5, 0) gives: 0 = a(1.5)^2 + b(1.5) + c
4. The point (-4, 0) gives: 0 = a(-4)^2 + b(-4) + c
By solving these equations simultaneously, you can find the values of a, b, and c. Once you have these values, you can analyze the parabola:
- Increase/Decrease: The parabola will be increasing to the left of the axis of symmetry, and decreasing to the right of the axis of symmetry.
- Positive/Negative: The parabola will be positive above the axis of symmetry (vertex), and negative below the axis of symmetry.
- Axis of Symmetry: The axis of symmetry can be found by the formula x = -b / (2a).
By plugging in the values of a and b, you can calculate the exact location of the vertex and the axis of symmetry.
Answered by
GPT 3.5
Based on the information provided:
1. The parabola decreases to the right of the axis of symmetry and increases to the left of the axis of symmetry.
2. The parabola is negative below the axis of symmetry and positive above the axis of symmetry.
3. To find the axis of symmetry x = -b / (2a), you need to determine the values of a and b from the given points.
- From points (-1.25, 15.125) and (0, 12), you can find the values of a and b.
- To find the axis of symmetry, you need to find the x-coordinate of the vertex, which is given by x = -b / (2a).
- Once you determine the values of a and b, plug them into the equation x = -b / (2a) to find the axis of symmetry.
If you need further assistance with calculating the specific values of a, b, and the axis of symmetry, feel free to provide the calculations you performed, and I can help you determine the precise results.
1. The parabola decreases to the right of the axis of symmetry and increases to the left of the axis of symmetry.
2. The parabola is negative below the axis of symmetry and positive above the axis of symmetry.
3. To find the axis of symmetry x = -b / (2a), you need to determine the values of a and b from the given points.
- From points (-1.25, 15.125) and (0, 12), you can find the values of a and b.
- To find the axis of symmetry, you need to find the x-coordinate of the vertex, which is given by x = -b / (2a).
- Once you determine the values of a and b, plug them into the equation x = -b / (2a) to find the axis of symmetry.
If you need further assistance with calculating the specific values of a, b, and the axis of symmetry, feel free to provide the calculations you performed, and I can help you determine the precise results.
Answered by
GPT 3.5
I apologize for the confusion in my previous responses. Let's clarify:
1. The parabola is opening downward, which means it will be decreasing to the left and increasing to the right of the axis of symmetry.
2. The values will be negative below the axis of symmetry and positive above the axis of symmetry.
3. To determine the axis of symmetry, you need to find the x-coordinate of the vertex, which is the point where the parabola changes direction from decreasing to increasing.
To sum up, in your case, the parabola will be increasing for the numbers on the right and decreasing for the numbers on the left. The axis of symmetry will be a vertical line that divides the parabola symmetrically and marks the transition between increasing and decreasing sections.
1. The parabola is opening downward, which means it will be decreasing to the left and increasing to the right of the axis of symmetry.
2. The values will be negative below the axis of symmetry and positive above the axis of symmetry.
3. To determine the axis of symmetry, you need to find the x-coordinate of the vertex, which is the point where the parabola changes direction from decreasing to increasing.
To sum up, in your case, the parabola will be increasing for the numbers on the right and decreasing for the numbers on the left. The axis of symmetry will be a vertical line that divides the parabola symmetrically and marks the transition between increasing and decreasing sections.
Answered by
GPT 3.5
No problem at all! I'm here to help clarify any questions you have.
If the vertex of the parabola is located at (-1.25, 15.125) at the very top (maximum point), then that point is indeed the vertex of the parabola.
For a parabola in the form y = ax^2 + bx + c that opens downward, the vertex serves as the axis of symmetry. This means that the axis of symmetry of the parabola will pass through the vertex point.
Therefore, in your case, the axis of symmetry of the parabola is the vertical line passing through the vertex at (-1.25, 15.125).
I hope this clears up any confusion. If you have any more questions or need further clarification, feel free to ask!
If the vertex of the parabola is located at (-1.25, 15.125) at the very top (maximum point), then that point is indeed the vertex of the parabola.
For a parabola in the form y = ax^2 + bx + c that opens downward, the vertex serves as the axis of symmetry. This means that the axis of symmetry of the parabola will pass through the vertex point.
Therefore, in your case, the axis of symmetry of the parabola is the vertical line passing through the vertex at (-1.25, 15.125).
I hope this clears up any confusion. If you have any more questions or need further clarification, feel free to ask!