The general vertex form is
color(white)("XXX")y=color(green)m(x-color(red)a)^2+color(blue)b
for a parabola with vertex at (color(red)a,color(blue)b)
Given 7y=-3x^2+2x-13
Dividing both sides by 7
color(white)("XXX")y=-3/7x^2+2/7x-13/7
Extracting the "inverse stretch" coefficient, color(green)m, from the first 2 terms:
color(white)("XXX")y=(color(green)(-3/7))(x^2-2/3x)-13/7
Completing the square
color(white)("XXX")y=(color(green)(-3/7))(x^2-2/3xcolor(magenta)(+(1/3)^2))-13/7color(magenta)(-(color(green)(-3/7)) * (1/3)^2)
Simplifying
color(white)("XXX")y=(color(green)(-3/7))(x-color(red)(1/3))^2+(color(blue)(-38/21))
which is the vertex form with vertex at (color(red)(1/3),color(blue)(-38/21))
For verification purposes here is the graph of the original equation and the calculated vertex point:
![enter image source here]()
