Question
a parabola on a grahp opens upward, and its vertex is -3,-10, so what is correct about this graph? Is th a-value negative? nope. Is the vertex at 3,-10? nope. but what about these two?
The c-value of the equation in standard form is −10
.
The c -value of the equation in standard form is negative 10 .
The c-value of the equation in standard form is −1
.
The c-value of the equation in standard form is −10
.
The c -value of the equation in standard form is negative 10 .
The c-value of the equation in standard form is −1
.
Answers
GPT-4o mini
In the context of a parabola described in standard form, which is given by the equation \(y = ax^2 + bx + c\), the c-value corresponds to the y-intercept of the graph.
Given that the vertex of the parabola is at (-3, -10), we know the following:
1. The parabola opens upward, which implies that the a-value is positive, so the first statement that "the a-value is negative" is incorrect.
2. The vertex is at (-3, -10), so the second statement that "the vertex is at (3, -10)" is also incorrect.
Now, evaluating the c-values:
- Since the vertex is at (-3, -10), the y-value of the vertex is -10. This value corresponds to the parabolic curve’s minimum point when the parabola opens upwards. However, the c-value specifically refers to the y-intercept of the parabola, which is found when \(x=0\).
- The c-value of the equation in standard form is not necessarily the same as the vertex's y-value; thus, while we know that one of the c-value statements could be misleading, if the parabola has a y-intercept somewhere different, we can't definitively state the c-value based solely on the vertex information given.
As for the specific statements:
1. "The c-value of the equation in standard form is −10." – **This statement could be true if the parabola intersects the y-axis at that point, but we don't know for sure without specific information on \(a\) and \(b\). It is not guaranteed.**
2. "The c-value of the equation in standard form is negative 10." – **This statement has the same implication as the first and it’s written differently, hence it’s the same assessment.**
3. "The c-value of the equation in standard form is −1." – **This statement contradicts possible values for c, assuming the y-intercept does not equal -1 without additional context.**
Thus, the true value of the c-value cannot be definitively determined without further information on the specific equation of the parabola.
Given that the vertex of the parabola is at (-3, -10), we know the following:
1. The parabola opens upward, which implies that the a-value is positive, so the first statement that "the a-value is negative" is incorrect.
2. The vertex is at (-3, -10), so the second statement that "the vertex is at (3, -10)" is also incorrect.
Now, evaluating the c-values:
- Since the vertex is at (-3, -10), the y-value of the vertex is -10. This value corresponds to the parabolic curve’s minimum point when the parabola opens upwards. However, the c-value specifically refers to the y-intercept of the parabola, which is found when \(x=0\).
- The c-value of the equation in standard form is not necessarily the same as the vertex's y-value; thus, while we know that one of the c-value statements could be misleading, if the parabola has a y-intercept somewhere different, we can't definitively state the c-value based solely on the vertex information given.
As for the specific statements:
1. "The c-value of the equation in standard form is −10." – **This statement could be true if the parabola intersects the y-axis at that point, but we don't know for sure without specific information on \(a\) and \(b\). It is not guaranteed.**
2. "The c-value of the equation in standard form is negative 10." – **This statement has the same implication as the first and it’s written differently, hence it’s the same assessment.**
3. "The c-value of the equation in standard form is −1." – **This statement contradicts possible values for c, assuming the y-intercept does not equal -1 without additional context.**
Thus, the true value of the c-value cannot be definitively determined without further information on the specific equation of the parabola.
okay, so i did notice that as the line curves upward towards the right it intersects at -1.