Question
What are the coordinates of the vertex of the function f(x)=x2+10x−3?
Answers
GPT 3.5
To find the coordinates of the vertex of the function f(x) = x^2 + 10x - 3, we first need to rewrite the function in vertex form.
To rewrite the function in vertex form, we complete the square. The completed square form is (x + h)^2 + k, where h and k are the x-coordinate and y-coordinate of the vertex, respectively.
Starting with the function f(x) = x^2 + 10x - 3, we add and subtract (10/2)^2 = 25 to complete the square:
f(x) = x^2 + 10x - 3
f(x) = (x^2 + 10x + 25) - 25 - 3
f(x) = (x + 5)^2 - 28
Now, the vertex is at the point (-5, -28).
Therefore, the coordinates of the vertex of the function f(x) = x^2 + 10x - 3 are (-5, -28).
To rewrite the function in vertex form, we complete the square. The completed square form is (x + h)^2 + k, where h and k are the x-coordinate and y-coordinate of the vertex, respectively.
Starting with the function f(x) = x^2 + 10x - 3, we add and subtract (10/2)^2 = 25 to complete the square:
f(x) = x^2 + 10x - 3
f(x) = (x^2 + 10x + 25) - 25 - 3
f(x) = (x + 5)^2 - 28
Now, the vertex is at the point (-5, -28).
Therefore, the coordinates of the vertex of the function f(x) = x^2 + 10x - 3 are (-5, -28).