y=x²-x-2 is a parabola open upward because the coefficient of x² is positive (=1)
hence it has a minimum.
To find the intercepts of this parabola with the x-axis, you have to find its roots by using the formula: x' = [- b + √(b² - 4ac)]/2a & x" =[- b - √(b² - 4ac)]/2a
a=1, b= -1 & c= -2. You will find x' =2 & x" = - 1
So the x-intercepts are (2,0) & ( - 1,0) & for y-intercepts you replace x by 0
& y intercept =-2 with coordinates (0, - 2)
Now To define vertex we have to find the axis of symmetry
The axis of symmetry is defined by x= -b/2a = -(-1)/2 = 1/2 so x =1/2
For the value of x=1/2 ==>y= -2 So Vertex(1/2, - 2.25) or vertex(1/2, -2¹/₄)
You have all the answers yo will check which one corresponds to our answer. Sorry the photo is hazy I can't read more what I did
