Y = x ^ 2-6x + 7 no formulário de vértice?

Responda:

$y = {(x - 3)}^{2} - 2$ $y=(x-3)^2-2$

Explicação:

$the equation of a parabola in vertex form$ $"the equation of a parabola in "color(blue)"vertex form"$ is.

$¯ ¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯ ¯ ∣ ∣ ∣ \frac{2}{2} y = a {(x - h)}^{2} + k \frac{2}{2} ∣ ∣ ∣ - ------------------- -$ $color(red)(bar(ul(|color(white)(2/2)color(black)(y=a(x-h)^2+k)color(white)(2/2)|)))$

$where (h, k) are the coordinates of the vertex and a$ $"where "(h,k)" are the coordinates of the vertex and a"$
$is a multiplier$ $"is a multiplier"$

$given the parabola in standard form; y = a x^{2} + b x + c$ $"given the parabola in "color(blue)"standard form";y=ax^2+bx+c$

$then the x-coordinate of the vertex is$ $"then the x-coordinate of the vertex is"$

$∙ x x_{vertex} = - \frac{b}{2 a}$ $•color(white)(x)x_(color(red)"vertex")=-b/(2a)$

$y = x^{2} - 6 x + 7 is in standard form$ $y=x^2-6x+7" is in standard form"$

$with a = 1, b = - 6 and c = 7$ $"with "a=1,b=-6" and "c=7$

$x_{vertex} = - \frac{- 6}{2} = 3$ $x_("vertex")=-(-6)/2=3$

$substitute this value into the equation for y$ $"substitute this value into the equation for y"$

$y_{vertex} = 9 - 18 + 7 = - 2$ $y_("vertex")=9-18+7=-2$

$(h, k) = (3, - 2)$ $(h,k)=(3,-2)$

$y = {(x - 3)}^{2} - 2 \leftarrow in vertex form$ $y=(x-3)^2-2larrcolor(red)"in vertex form"$