To determine which function is equivalent, let's start by trying to factor the given quadratic function or express it in vertex form:
g(k) = -k^2 + 6k - 9
The vertex form of a quadratic function is:
g(k) = a*(k - h)^2 + k, where (h, k) is the vertex of the parabola.
First, we can complete the square to put g(k) in vertex form:
g(k) = -(k^2 - 6k) - 9
To complete the square, take half of the coefficient of k (which is 6), square it, and add it inside the parenthesis. We have to add the same value outside the parenthesis multiplied by -1 since there's a negative sign outside the parenthesis:
(6/2)^2 = 3^2 = 9
We add and subtract 9 inside the parenthesis to complete the square:
g(k) = -(k^2 - 6k + 9) - 9 + 9
g(k) = -(k - 3)^2 - 9 + 9
g(k) = -(k - 3)^2
And since -9 + 9 cancels out to be 0, the equivalent function in vertex form is:
g(k) = -(k - 3)^2
Among the given options, the equivalent function to g(k) = -k^2 + 6k - 9 is:
g(k) = -(k - 3)^2
Therefore, the correct response is:
g(k) = -(k - 3)^2
Which function is equivalent to g(k) = -k^2 + 6k - 9?
Responses:
g(k) = - (k-3)^2
g(k) = (-k + 3)(k + 3)
g(k) = - (k + 3)^2
g(k) = (-k - 3)( - k + 3)
1 answer
1 answer