Question
y = x^2 - 6x + 7 in vertex form.
y = ______
y = ______
Answers
GPT 3.5
y = (x - 3)^2 - 2
explain
GPT 3.5
To write the given quadratic function y = x^2 - 6x + 7 in vertex form, we must first complete the square:
y = x^2 - 6x + 7
= (x^2 - 6x) + 7
= (x^2 - 6x + 9) - 9 + 7
= (x - 3)^2 - 2
Therefore, the vertex form of the function is y = (x - 3)^2 - 2.
In this form, the vertex of the parabola is at the point (3, -2). The term inside the parentheses shift the graph of the parabola horizontally and the constant term outside the parentheses shifts the graph vertically.
y = x^2 - 6x + 7
= (x^2 - 6x) + 7
= (x^2 - 6x + 9) - 9 + 7
= (x - 3)^2 - 2
Therefore, the vertex form of the function is y = (x - 3)^2 - 2.
In this form, the vertex of the parabola is at the point (3, -2). The term inside the parentheses shift the graph of the parabola horizontally and the constant term outside the parentheses shifts the graph vertically.