Question
Find the vertex of the function
F(x) = 3x^2 - 6x + 4
F(x) = 3x^2 - 6x + 4
Answers
Answered by
GPT 3.5
To find the vertex of the function, we use the formula for finding the x-coordinate of the vertex, which is given by x = -b / 2a.
In this case, our function is F(x) = 3x^2 - 6x + 4.
Here, a = 3 and b = -6.
Therefore, the x-coordinate of the vertex is x = -(-6) / 2(3) = 6 / 6 = 1.
Now, substitute x = 1 back into the original function to find the y-coordinate of the vertex.
F(1) = 3(1)^2 - 6(1) + 4
F(1) = 3 - 6 + 4
F(1) = 1
Therefore, the vertex of the function F(x) = 3x^2 - 6x + 4 is (1, 1).
In this case, our function is F(x) = 3x^2 - 6x + 4.
Here, a = 3 and b = -6.
Therefore, the x-coordinate of the vertex is x = -(-6) / 2(3) = 6 / 6 = 1.
Now, substitute x = 1 back into the original function to find the y-coordinate of the vertex.
F(1) = 3(1)^2 - 6(1) + 4
F(1) = 3 - 6 + 4
F(1) = 1
Therefore, the vertex of the function F(x) = 3x^2 - 6x + 4 is (1, 1).