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A parabola is graphed on a coordinate plane. The x-axis ranges from negative 10 to 3 in increments of 1. The y-axis ranges from negative 10 to 10 in increments of 1.
Which of the following is true based on the graph of the quadratic?
(1 point)
Responses
The c-value of the equation in standard form is −10
.
The c -value of the equation in standard form is negative 10 .
The a-value is negative.
The a -value is negative.
The c-value of the equation in standard form is −1
.
The c -value of the equation in standard form is negative 1 .
The vertex is located at (3,−10)
A parabola is graphed on a coordinate plane. The x-axis ranges from negative 10 to 3 in increments of 1. The y-axis ranges from negative 10 to 10 in increments of 1.
Which of the following is true based on the graph of the quadratic?
(1 point)
Responses
The c-value of the equation in standard form is −10
.
The c -value of the equation in standard form is negative 10 .
The a-value is negative.
The a -value is negative.
The c-value of the equation in standard form is −1
.
The c -value of the equation in standard form is negative 1 .
The vertex is located at (3,−10)
Answers
There are no human answers yet.
Answered by
GPT-4o mini
To determine which statement is true regarding the graph of the parabola, we need to consider a few characteristics of parabolas:
1. The **c-value** in the standard form of a quadratic equation \( y = ax^2 + bx + c \) represents the y-intercept of the graph, which is the point where the graph intersects the y-axis (when \( x = 0 \)).
2. The **a-value** determines the direction (upwards if \( a > 0 \) and downwards if \( a < 0 \)) and the width of the parabola.
3. The **vertex** of the parabola is its highest or lowest point, depending on the direction it opens.
From the information provided:
- If the graph shows the parabola intersects the y-axis at (0, -10), then the c-value is indeed -10.
- If the parabola opens downwards, the a-value is negative.
- If the vertex is shown to be at (3, -10), that would contradict the typical calculations, as the vertex’s x-value being greater than the y-intercept at (0, -10) suggests a different location.
Based on these observations:
1. If the parabola intersects the y-axis at (0, -10), then **the c-value in standard form is -10** is true.
2. If the parabola opens downwards (typical of a negative a-value), then **the a-value is negative** is also true.
3. If the vertex is at (3, -10), this would likely be incorrect considering the location of the y-intercept unless it is defined as such by the specific graph.
To answer your query without visual confirmation, the most certain statement would likely be:
- **The c-value of the equation in standard form is −10.**
1. The **c-value** in the standard form of a quadratic equation \( y = ax^2 + bx + c \) represents the y-intercept of the graph, which is the point where the graph intersects the y-axis (when \( x = 0 \)).
2. The **a-value** determines the direction (upwards if \( a > 0 \) and downwards if \( a < 0 \)) and the width of the parabola.
3. The **vertex** of the parabola is its highest or lowest point, depending on the direction it opens.
From the information provided:
- If the graph shows the parabola intersects the y-axis at (0, -10), then the c-value is indeed -10.
- If the parabola opens downwards, the a-value is negative.
- If the vertex is shown to be at (3, -10), that would contradict the typical calculations, as the vertex’s x-value being greater than the y-intercept at (0, -10) suggests a different location.
Based on these observations:
1. If the parabola intersects the y-axis at (0, -10), then **the c-value in standard form is -10** is true.
2. If the parabola opens downwards (typical of a negative a-value), then **the a-value is negative** is also true.
3. If the vertex is at (3, -10), this would likely be incorrect considering the location of the y-intercept unless it is defined as such by the specific graph.
To answer your query without visual confirmation, the most certain statement would likely be:
- **The c-value of the equation in standard form is −10.**
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