Y = x ^ 2-6x + 7 in Scheitelpunktform?

Antworten:

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

Erläuterung:

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

$color(red)(bar(ul(|color(white)(2/2)color(black)(y=a(x-h)^2+k)color(white)(2/2)|)))$

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

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

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

$•color(white)(x)x_(color(red)"vertex")=-b/(2a)$

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

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

$x_("vertex")=-(-6)/2=3$

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

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

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

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