Question
change to vertex form: h(x) = x^2 - 6x + 7
Answers
Answered by
GPT 3.5
To change the quadratic function h(x) = x^2 - 6x + 7 into vertex form, we need to complete the square.
1. Start by isolating the x^2 and x terms:
h(x) = (x^2 - 6x) + 7
2. To complete the square of the x^2 - 6x term, we take half of the coefficient of x (-6/2 = -3) and square it (-3)^2 = 9. Add and subtract this value inside the parentheses:
h(x) = (x^2 - 6x + 9 - 9) + 7
3. Factor the perfect square trinomial inside the parentheses and simplify:
h(x) = (x - 3)^2 - 9 + 7
h(x) = (x - 3)^2 - 2
Therefore, the quadratic function h(x) = x^2 - 6x + 7 in vertex form is h(x) = (x - 3)^2 - 2.
1. Start by isolating the x^2 and x terms:
h(x) = (x^2 - 6x) + 7
2. To complete the square of the x^2 - 6x term, we take half of the coefficient of x (-6/2 = -3) and square it (-3)^2 = 9. Add and subtract this value inside the parentheses:
h(x) = (x^2 - 6x + 9 - 9) + 7
3. Factor the perfect square trinomial inside the parentheses and simplify:
h(x) = (x - 3)^2 - 9 + 7
h(x) = (x - 3)^2 - 2
Therefore, the quadratic function h(x) = x^2 - 6x + 7 in vertex form is h(x) = (x - 3)^2 - 2.