• The graph has a maximum at (1,11).
• The graph has a y-intercept at (0,9).
• The function in vertex form is f(x) = -2(x-1)^2 + 11
Which are true about the
function f (x) = -2x^2 + 4x + 9? Select all that
apply.
(3 points)
• The graph has a minimum at (1,7).
• The graph has a maximum at (1,7).
• The graph has a maximum at (1,11).
• The graph has a y-intercept at (0,9).
• The graph has a y-intercept at (0,-9).
• The function in vertex form is
f(x) = -2(x-1)^2 + 7
• The function in vertex form is
f(x) = -2(x-1)^2 + 11
7 answers
are you sure
I apologize for the error in my response. Let's reevaluate the given function f(x) = -2x^2 + 4x + 9.
The equation is in the form f(x) = ax^2 + bx + c, where a = -2, b = 4, and c = 9.
To find the vertex of the parabola represented by this quadratic function, we use the formula x = -b / (2a).
In this case, x = -4 / (2 * -2) = -4 / -4 = 1.
Plug x = 1 into the function to find the corresponding y-coordinate:
f(1) = -2(1)^2 + 4(1) + 9 = -2 + 4 + 9 = 11.
Therefore, the vertex of the graph is at (1, 11). So, the statement "The graph has a maximum at (1,11)" is an accurate statement. With this information, we can proceed with reviewing the other options:
• The graph has a minimum at (1,7). - FALSE
• The graph has a maximum at (1,7). - FALSE
• The graph has a maximum at (1,11). - TRUE
• The graph has a y-intercept at (0,9). - TRUE
• The graph has a y-intercept at (0,-9). - FALSE
• The function in vertex form is f(x) = -2(x-1)^2 + 7 - FALSE
• The function in vertex form is f(x) = -2(x-1)^2 + 11 - TRUE
Therefore, the correct statements are:
• The graph has a maximum at (1,11).
• The graph has a y-intercept at (0,9).
• The function in vertex form is f(x) = -2(x-1)^2 + 11.
The equation is in the form f(x) = ax^2 + bx + c, where a = -2, b = 4, and c = 9.
To find the vertex of the parabola represented by this quadratic function, we use the formula x = -b / (2a).
In this case, x = -4 / (2 * -2) = -4 / -4 = 1.
Plug x = 1 into the function to find the corresponding y-coordinate:
f(1) = -2(1)^2 + 4(1) + 9 = -2 + 4 + 9 = 11.
Therefore, the vertex of the graph is at (1, 11). So, the statement "The graph has a maximum at (1,11)" is an accurate statement. With this information, we can proceed with reviewing the other options:
• The graph has a minimum at (1,7). - FALSE
• The graph has a maximum at (1,7). - FALSE
• The graph has a maximum at (1,11). - TRUE
• The graph has a y-intercept at (0,9). - TRUE
• The graph has a y-intercept at (0,-9). - FALSE
• The function in vertex form is f(x) = -2(x-1)^2 + 7 - FALSE
• The function in vertex form is f(x) = -2(x-1)^2 + 11 - TRUE
Therefore, the correct statements are:
• The graph has a maximum at (1,11).
• The graph has a y-intercept at (0,9).
• The function in vertex form is f(x) = -2(x-1)^2 + 11.
please double check
Certainly! Let's revisit the function f(x) = -2x^2 + 4x + 9 and reevaluate the given options:
1. The graph has a minimum at (1,7): Let's first find the vertex of the parabola.
The x-coordinate of the vertex is given by x = -b / (2a) = -4 / (2*(-2)) = -4 / -4 = 1.
Substitute x = 1 into the function to find the y-coordinate:
f(1) = -2(1)^2 + 4(1) + 9 = -2 + 4 + 9 = 11.
The vertex is at (1, 11), not (1, 7). Therefore, this statement is FALSE.
2. The graph has a maximum at (1,7): This statement is not possible since the vertex is actually a minimum at (1, 11). Therefore, this statement is FALSE.
3. The graph has a maximum at (1,11): As calculated above, the vertex occurs at (1, 11), making this statement TRUE.
4. The graph has a y-intercept at (0,9): To find the y-intercept, plug x = 0 into the function:
f(0) = -2(0)^2 + 4(0) + 9 = 0 + 0 + 9 = 9.
Therefore, the graph has a y-intercept at (0, 9), making this statement TRUE.
5. The graph has a y-intercept at (0,-9): This statement is FALSE, as proven above.
6. The function in vertex form is f(x) = -2(x-1)^2 + 7: This statement is FALSE since the correct vertex form is f(x) = -2(x-1)^2 + 11.
7. The function in vertex form is f(x) = -2(x-1)^2 + 11: This statement is TRUE, as determined earlier.
Therefore, the correct statements are:
• The graph has a maximum at (1,11).
• The graph has a y-intercept at (0,9).
• The function in vertex form is f(x) = -2(x-1)^2 + 11.
Thank you for encouraging a check and ensuring accuracy.
1. The graph has a minimum at (1,7): Let's first find the vertex of the parabola.
The x-coordinate of the vertex is given by x = -b / (2a) = -4 / (2*(-2)) = -4 / -4 = 1.
Substitute x = 1 into the function to find the y-coordinate:
f(1) = -2(1)^2 + 4(1) + 9 = -2 + 4 + 9 = 11.
The vertex is at (1, 11), not (1, 7). Therefore, this statement is FALSE.
2. The graph has a maximum at (1,7): This statement is not possible since the vertex is actually a minimum at (1, 11). Therefore, this statement is FALSE.
3. The graph has a maximum at (1,11): As calculated above, the vertex occurs at (1, 11), making this statement TRUE.
4. The graph has a y-intercept at (0,9): To find the y-intercept, plug x = 0 into the function:
f(0) = -2(0)^2 + 4(0) + 9 = 0 + 0 + 9 = 9.
Therefore, the graph has a y-intercept at (0, 9), making this statement TRUE.
5. The graph has a y-intercept at (0,-9): This statement is FALSE, as proven above.
6. The function in vertex form is f(x) = -2(x-1)^2 + 7: This statement is FALSE since the correct vertex form is f(x) = -2(x-1)^2 + 11.
7. The function in vertex form is f(x) = -2(x-1)^2 + 11: This statement is TRUE, as determined earlier.
Therefore, the correct statements are:
• The graph has a maximum at (1,11).
• The graph has a y-intercept at (0,9).
• The function in vertex form is f(x) = -2(x-1)^2 + 11.
Thank you for encouraging a check and ensuring accuracy.
CHECK AGAIN FOR YOUR FINAL ANSWER
Let's reevaluate the function f(x) = -2x^2 + 4x + 9 and the given options:
1. The graph has a minimum at (1,7): To find the minimum value of the function, we first determine the vertex.
The x-coordinate of the vertex is given by x = -b / (2a) = -4 / (2*(-2)) = 1.
Substitute x = 1 into the function to find the y-coordinate:
f(1) = -2(1)^2 + 4(1) + 9 = -2 + 4 + 9 = 11.
Therefore, the vertex is at (1, 11), not (1, 7). This statement is FALSE.
2. The graph has a maximum at (1,7): Since the vertex is (1, 11), this statement is FALSE.
3. The graph has a maximum at (1,11): The vertex is at (1, 11), which is a maximum point. This statement is TRUE.
4. The graph has a y-intercept at (0,9): To find the y-intercept, plug x = 0 into the function:
f(0) = -2(0)^2 + 4(0) + 9 = 0 + 0 + 9 = 9.
The graph has a y-intercept at (0, 9), making this statement TRUE.
5. The graph has a y-intercept at (0,-9): This statement is FALSE.
6. The function in vertex form is f(x) = -2(x-1)^2 + 7: This statement is FALSE.
7. The function in vertex form is f(x) = -2(x-1)^2 + 11: This statement is TRUE.
Therefore, the correct statements are:
• The graph has a maximum at (1,11).
• The graph has a y-intercept at (0,9).
• The function in vertex form is f(x) = -2(x-1)^2 + 11.
Thank you for your patience.
1. The graph has a minimum at (1,7): To find the minimum value of the function, we first determine the vertex.
The x-coordinate of the vertex is given by x = -b / (2a) = -4 / (2*(-2)) = 1.
Substitute x = 1 into the function to find the y-coordinate:
f(1) = -2(1)^2 + 4(1) + 9 = -2 + 4 + 9 = 11.
Therefore, the vertex is at (1, 11), not (1, 7). This statement is FALSE.
2. The graph has a maximum at (1,7): Since the vertex is (1, 11), this statement is FALSE.
3. The graph has a maximum at (1,11): The vertex is at (1, 11), which is a maximum point. This statement is TRUE.
4. The graph has a y-intercept at (0,9): To find the y-intercept, plug x = 0 into the function:
f(0) = -2(0)^2 + 4(0) + 9 = 0 + 0 + 9 = 9.
The graph has a y-intercept at (0, 9), making this statement TRUE.
5. The graph has a y-intercept at (0,-9): This statement is FALSE.
6. The function in vertex form is f(x) = -2(x-1)^2 + 7: This statement is FALSE.
7. The function in vertex form is f(x) = -2(x-1)^2 + 11: This statement is TRUE.
Therefore, the correct statements are:
• The graph has a maximum at (1,11).
• The graph has a y-intercept at (0,9).
• The function in vertex form is f(x) = -2(x-1)^2 + 11.
Thank you for your patience.
1 answer