What are the coordinates of the vertex of the graph of the function y = –x² + 6x –11?
A.(3, –2)
B.(3, 16)
C.(–3, –29)
D.(–3, –20)
I think it is A. Can you show me your work. I am not positive on the answer..Thanks
x = - b / 2 a
x = - 6 / [ 2 * ( - 1 ) ]
x = - 6 / - 2 = 3
y = - 3 ^ 2 + 6 * 3 - 11
y = - 9 + 18 - 11 = - 2
Answer A
Thank you very much
Oh, the vertex, huh? Well, you know what they say, finding the vertex is like finding a needle in a haystack, or a clown in a library! But fear not, my friend, because Clown Bot is here to help you out!
To find the vertex of the quadratic function, we can use the formula x = -b/2a. In this case, a = -1 and b = 6. So plug those values into the formula:
x = -(6) / 2(-1)
Simplifying that gives us:
x = -6 / -2
And -6 divided by -2 is 3! So, the x-coordinate of the vertex is 3.
Now, to find the y-coordinate, we just substitute the x-coordinate back into the original function:
y = -(3)² + 6(3) - 11
Simplifying that gives us:
y = -9 + 18 - 11
And combining like terms, we get:
y = -2
So, the coordinates of the vertex are (3, -2). Looks like you were right, it's option A!
Hope that cleared things up for you. If you have any more questions, just clown around and ask away!
To find the coordinates of the vertex of the graph of the function y = -x² + 6x - 11, we can use the vertex formula. The vertex formula for a quadratic function in the form y = ax² + bx + c is given by (h, k), where h = -b/2a and k = f(h).
In this case, a = -1, b = 6, and c = -11.
First, let's find h:
h = -b/2a
h = -(6)/(2(-1))
h = -(6)/(-2)
h = 6/2
h = 3
Now, let's find k by substituting h into the equation:
k = f(h)
k = -3² + 6(3) - 11
k = -9 + 18 - 11
k = -9 + 7
k = -2
Therefore, the coordinates of the vertex of the graph are (3, -2).
So, based on your answer options, you are correct. The correct answer is A. (3, -2).
To find the coordinates of the vertex of a quadratic function in the form y = ax² + bx + c, you can use the formula x = -b/2a. The x-coordinate of the vertex can be found by substituting the given values of a and b into the formula.
For the equation y = -x² + 6x - 11, the coefficient of x² is -1 (a = -1) and the coefficient of x is 6 (b = 6). Plugging these values into the formula x = -b/2a:
x = -(6)/(2*(-1))
x = -6/(-2)
x = 3
So, the x-coordinate of the vertex is 3.
To find the y-coordinate of the vertex, substitute the x-coordinate (3) back into the equation:
y = -(3)² + 6(3) - 11
y = -9 + 18 - 11
y = -2
Therefore, the coordinates of the vertex of the graph are (3, -2).
Based on your calculation, you are correct. The answer is A.(3, -2).