Answer:
(x - 3)² - 2
Step-by-step explanation:
The equation of a parabola in vertex form is
y = a(x - h)² + k
where (h, k) are the coordinates of the vertex and a is a multiplier
Given a parabola in standard form : ax² + bx + c : a ≠ 0
Then the x- coordinate of the vertex is
[tex]x_{vertex}[/tex] = - [tex]\frac{b}{2a}[/tex]
y = x² - 6x + 7 is in standard form
with a = 1, b = - 6, c = 7, hence
[tex]x_{vertex}[/tex] = - [tex]\frac{-6}{2}[/tex] = 3
substitute x = 3 into the equation for corresponding value of
y = 3² - 6(3) + 7 = 9 - 18 + 7 = - 2
(h, k) = (3, - 2), hence
y = (x - 3)² - 2 ← in vertex form
