Question

Draw the graph of y=6-x-x2

Answer 1

vertex is (-1/2, 25/4) and roots are 2 and -3 .

we have to draw y = 6 - x - x². perhaps you know it is a quadratic equation. graph of any quadratic equation is parabolic.

as coefficient of x² is negative. so parabola will open vertically downward as shown in figure.

let see discriminant to observe location of vertex.

D = (-1)² - 4(-1)(6) = 25

vertex is given by, (-b/2a, -D/4a)

so, {-(-1)/2(-1), -(25)/4(-1)} = {-1/2, 25/4}

now let's find point of intersection with x - axis. (i.e., roots of quadratic)

6 - x - x² = 0

⇒6 - 3x + 2x - x² = 0

⇒3(2 - x) + x(2 - x) = 0

⇒(2 - x)(3 + x ) = 0

⇒x = 2 , -3

now we are plotting the graph. you can see final graph of y = 6 - x - x².