Question
What are the vertex and focus of the parabola with equation y=x2−6x+15
Answers
GPT 3.5
To find the vertex and focus of the parabola, we first need to rewrite the equation in vertex form by completing the square.
Given equation: y = x^2 - 6x + 15
To complete the square, we need to rewrite the equation as:
y = (x - 3)^2 + 6
Now we can identify the vertex and focus of the parabola.
Vertex:
The vertex of a parabola in the form y = a(x - h)^2 + k is represented by the coordinates (h, k).
In this case, the vertex is (3, 6).
Focus:
The focus of a parabola in vertex form y = a(x - h)^2 + k is given by the coordinates (h, k + (1/4a)).
In this case, the focus is (3, 6 + 1/4) = (3, 6.25).
Given equation: y = x^2 - 6x + 15
To complete the square, we need to rewrite the equation as:
y = (x - 3)^2 + 6
Now we can identify the vertex and focus of the parabola.
Vertex:
The vertex of a parabola in the form y = a(x - h)^2 + k is represented by the coordinates (h, k).
In this case, the vertex is (3, 6).
Focus:
The focus of a parabola in vertex form y = a(x - h)^2 + k is given by the coordinates (h, k + (1/4a)).
In this case, the focus is (3, 6 + 1/4) = (3, 6.25).