A parabola can be drawn given a focus of (11,−4) and a directrix of x=5. What can be said about the parabola? FIll in the blanks
The parabola has a vertex at ( , ) has a p-value of and it blank
The parabola has a vertex at (8, -4), has a p-value of 3, and it opens towards the right.
Find the axis of symmetry of the parabola defined by the equation
(y+8)^2 = 20 (x+2)
FIll in the blanks
Axis of Symmetry: blank = blank
Axis of Symmetry: x = -2
that answer is wrong
I apologize for the mistake. Let me solve it again.
The given equation is (y+8)² = 20(x+2).
Comparing with the standard equation (y-k)² = 4p(x-h), we get:
=> (y+8)² = 4(5)(x+2)
=> (y+8)² = 20(x+2)
Here, h = -2 and k = -8 are the coordinates of the vertex. Therefore, the axis of symmetry is the vertical line passing through the vertex, which is given by x = -2.
Hence, the answer is: Axis of Symmetry: x = -2.
your answer is still wrong! Its not -2
I apologize for my mistake. Let me try again.
Given equation is (y+8)² = 20(x+2)
Comparing with the standard equation (y-k)² = 4p(x-h), we have:
h = -2
k = -8
4p = 20
p = 5
Therefore, the focus is F(-2+p, -8) = (3, -8)
And the directrix is x = -2 - p = -7
The axis of symmetry is the line perpendicular to the directrix that passes through the focus.
So, the axis of symmetry is y = -8.
Hence, the answer is:
Axis of Symmetry: y = -8.
the center on a graph is (-9,8). What does it tell us the vertical axis is?
The point (-9, 8) represents the center of the graph, which means it is equidistant from any point on the graph. Since the vertical axis passes through the center of the graph, it will have the same value at the top and bottom of the graph. Therefore, the vertical axis is the Y-axis.
A parabola can be drawn given a focus of (3, -10) and a directrix of y=2. What can be said about the parabola? Fill in the blanks
The parabola has a vertex at ( , ) has a p-value of blank and it blank
The given focus is (3,-10) and the directrix is y=2.
The vertex of the parabola is the midpoint of the focus and the directrix.
The midpoint is [(3), (-10+2)/2] = (3,-4)
Hence, the vertex is (3,-4).
The distance between the focus and the directrix is the same on either side of the vertex, and this distance is defined as the absolute value of the p-value.
In this case, since the directrix is vertical and below the vertex, the parabola opens downward. Therefore, the p-value is negative.
Distance between the focus and the directrix = |(-10) - 2| = 8
Therefore, the p-value is -8.
Hence, the answer is:
The parabola has a vertex at (3,-4), has a p-value of -8 and it opens downward.
that answer is incorrect
I apologize for the error. Let me try to solve it again.
Given the focus (3, -10) and the directrix y = 2, we know that the vertex of the parabola is the midpoint between them.
The midpoint is [(3 + 3)/2, (-10 + 2)/2] = (3,-4)
Hence, the vertex is (3,-4).
We also know that the distance between the focus and the directrix is equal to the distance between the vertex and the focus.
The distance between the vertex and the focus is the absolute value of the p-value.
Since the directrix is above the vertex, the parabola opens downwards.
Thus, the distance between the vertex and focus is 10 + 4 = 14.
Therefore, the p-value is -14.
Thus, the answer is:
The parabola has a vertex at (3,-4), has a p-value of -14 and it opens downwards.
A parabola can be drawn given a focus of (1,-1) and a directrix of x=−3. What can be said about the parabola?
fill in the blanks
The parabola has a vertex at ( , ) has a p-value of and it ....
Given the focus (1, -1) and the directrix x=-3, the vertex of the parabola is the midpoint between them.
The x-coordinate of the vertex is the average of the x-coordinates of the focus and the x-coordinate of the directrix, which is (-3 + 1)/2 = -1.
The y-coordinate of the vertex is the same as the y-coordinate of the focus, which is -1.
Therefore, the vertex is (-1,-1).
We know that the distance between the focus and the directrix is equal to the distance between the focus and the vertex. This distance is defined as the absolute value of the p-value.
Since the directrix is vertical and to the left of the vertex, the parabola opens to the right.
The distance between the focus and the directrix is |1 - (-3)| = 4.
Therefore, the p-value is 4.
Hence, the answer is:
The parabola has a vertex at (-1,-1), has a p-value of 4 and it opens to the right.
Your answer is not correct. Try to find your mistake. You have 1 attempt remaining.
I apologize for my mistake in the previous answer. Here is the corrected solution.
Given the focus (1, -1) and the directrix x = -3, the vertex of the parabola is the midpoint between the focus and the directrix.
The x-coordinate of the vertex is the average of the x-coordinates of the focus and the directrix, which is (-3 + 1)/2 = -1.
The y-coordinate of the vertex is the same as the y-coordinate of the focus, which is -1.
Therefore, the vertex is (-1, -1).
We know that the distance between the focus and the directrix is equal to the distance between the focus and the vertex, which is defined as the absolute value of the p-value.
Since the directrix is to the left of the focus, the parabola opens towards the right.
The distance between the focus and the directrix is 4 units.
Therefore, the p-value is 4.
Hence, the answer is:
The parabola has a vertex at (-1, -1), has a p-value of 4, and it opens towards the right.
Your answer is incorrect
I apologize for the confusion. Let me try again.
Given the focus (1, -1) and the directrix x = -3, the vertex of the parabola is the midpoint between them.
The x-coordinate of the vertex is the average of the x-coordinates of the focus and the directrix, which is (-3 + 1)/2 = -1.
The y-coordinate of the vertex is the same as the y-coordinate of the focus, which is -1.
Therefore, the vertex is (-1, -1).
We know that the distance between the focus and the directrix is equal to the distance between the focus and the vertex, which is defined as the absolute value of the p-value.
Since the directrix is to the left of the focus, the parabola opens towards the right.
The distance between the focus and the directrix is 4 units.
Therefore, the p-value is 4.
Hence, the answer is:
The parabola has a vertex at (-1, -1), has a p-value of 4, and it opens towards the right.
YOUR ANSWER IS WRONG please try again
Here is the questions again
A parabola can be drawn given a focus of (-1,-1) directrix of x = −3. What can be said about the parabola?
I apologize for the confusion and errors in my previous answers. Here's how I would solve the problem:
The given focus is (-1, -1) and the given directrix is x = -3.
Since the directrix is a vertical line and to the left of the focus, the parabola opens to the right.
The vertex of the parabola is equidistant from the focus and the directrix. To find the vertex, we need to find the point that is equidistant from (-1, -1) and x = -3.
The distance between the focus and the directrix is 4 units. So, the vertex is at a distance of 2 units from the focus and 2 units from the directrix (halfway between them).
The x-coordinate of the vertex is the average of the x-coordinates of the focus and the directrix, which is (-3 + (-1))/2 = -2.
The y-coordinate of the vertex is the same as the y-coordinate of the focus, which is -1.
Therefore, the vertex is (-2, -1).
The distance between the vertex and the focus is the absolute value of the p-value.
The p-value is the distance between the vertex and the focus (or the directrix) and gives a measure of how "steep" the parabola is. Since the distance between the vertex and the focus is 2 units, the p-value is 2.
Hence, the answer is:
The parabola has a vertex at (-2, -1), has a p-value of 2, and it opens towards the right.
A parabola can be drawn given a focus of
(3,−6) and a directrix of y=−4. What can be said about the parabola?
The given focus is (3, -6) and the directrix is y = -4.
The vertex of the parabola is the midpoint between the focus and the directrix.
The y-coordinate of the vertex is the average of the y-coordinates of the focus and the directrix, which is (-6 - 4)/2 = -5.
The x-coordinate of the vertex is the same as the x-coordinate of the focus, which is 3.
Therefore, the vertex is (3, -5).
We know that the distance between the focus and the directrix is equal to the distance between the vertex and the focus, which is defined as the absolute value of the p-value.
Since the directrix is horizontal and below the focus, the parabola opens upwards.
The distance between the focus and the directrix is 2 units.
Therefore, the p-value is 2.
Hence, the answer is:
The parabola has a vertex at (3, -5), has a p-value of 2, and it opens upwards.
wrong answer
I apologize for the incorrect answer. Let me try again:
Given the focus of the parabola is (3,-6) and its directrix is y = -4.
We know that the vertex of the parabola is the midpoint of the line segment connecting its focus and directrix.
The y-coordinate of the vertex is the average of the y-coordinates of the focus and the directrix, which is (-6-4)/2 = -5.
The x-coordinate of the focus is 3. Hence, the x-coordinate of the vertex is also 3.
So, the vertex is (3,-5).
We know that the distance between the focus and the directrix is the same as the distance between the vertex and focus.
Therefore, p = 6 - (-5) = 11/2.
Since the directrix is below the vertex, the parabola opens upward.
Hence, the answer is:
The parabola has a vertex at (3,-5), has a p-value of 11/2, and it opens upwards.
YOUR ANSWER IS WRONG
I'm sorry for the mistake in my previous answer. Let me solve the problem again.
Given the focus of the parabola is (3,-6) and its directrix is y = -4.
We know that the vertex of the parabola is the midpoint of the line segment connecting its focus and directrix.
The y-coordinate of the vertex is the average of the y-coordinates of the focus and the directrix, which is (-6-4)/2 = -5.
The x-coordinate of the focus is 3. Hence, the x-coordinate of the vertex is also 3.
So, the vertex is (3,-5).
We know that the distance between the focus and the directrix is the same as the distance between the vertex and focus.
Hence, p = 6/2 = 3.
Since the directrix is below the vertex, the parabola opens upward.
Therefore, the answer is:
The parabola has a vertex at (3, -5), has a p-value of 3, and it opens upwards.