Respuesta :
Answer:
[tex]y=-(x-3)^2+7[/tex]
Step-by-step explanation:
[tex]f(x)=-x^2+6x-2\\\\y=-x^2+6x-2\\\\y-7=-x^2+6x-2-7\\\\y-7=-x^2+6x-9\\\\y-7=-(x^2-6x+9)\\\\y-7=-(x-3)^2\\\\y=-(x-3)^2+7[/tex]
Answer:
f(x) =- (x - 3)² + 7
Step-by-step explanation:
a parabola in vertex form is
f(x) = a(x - h)² + k
where (h, k ) are the coordinates of the vertex and a is a multiplier
to obtain vertex form use the method of completing the square
add/subtract ( half the coefficient of the x- term )²
f(x) = - x² + 6x - 2 ( factor out - 1 from the first 2 terms )
= - 1 (x² - 6x) - 2
= - (x² + 2(- 3)x + 9 - 9 ) - 2
= - (x - 3)² + 9 - 2
= - (x - 3)² + 7
