Acard is drawn from a standard 52-card deck. what is the probability that the card is a red 8, given that the card is an 8?

there are 2 red 8's in a deck so it would be 2/52 which can be reduced to a

 1/26 probability

the formula is x = -b/(2a), where the parabola is of the form y = ax^2 + bx + c.

we can derive this by completing the square

y = ax^2 + bx + c

= a(x^2 + (b/a)x   ) + c

= a(x^2 + (b/a)x + (b/(2a))^2 - (b/(2a))^2   ) + c

= a( (x + b/(2a) )^2 - (b/(2a))^2 ) + c

= a(x + b/(2a) )^2 - a(b/2a)^2 + c

or by using calculus which uses the fact that that , so the critical point (always a global maximum or minimum in the case of a parabola) occurs at x = -b/(2a).

the one difference between alex's construction steps and brittanie's construction steps is that, in case of alex she need to draw a perpendicular bisector of diameter but in case of britannie she need to draw arc from center on the circle.

step to step explanation: -

to construct inscribed square we need to draw a circle and then draw construct diameter in the circle then construct perpendicular bisector of diameter which intersect the circle.by using straightedge draw lines joining both the end points of diameter to intersection points made by perpendicular bisector on circle.

to construct inscribed equilateral triangle we need to draw a circle with radius r and then use compass to draw arc from center on the circle. use the same setting of compass . put the compass on the intersection point of arc on the circle and draw another arc from there on the circle.continue this to draw third arc on the circle.use straightedge to join all the intersections of arc with the circle.