how do I do this please respond quickly

Question

in algebra we have a project regarding parabolas. we had this equation y=-x^2-2x+15. what are the roots of this equation and how do I figure that out. also what are 3 points i should plot on the graph besides the y intercept.  

 

thanks 

Answer 1

To solve for the roots you can use quadratic equation. So x=(-b +/- (sqrt(b^2-4ac)))/(2a). Here a=-1, b=-2, and c=15. Plugging this in we get x= (-(-2) +/- (sqrt((-2)^2 - 4*-1*15))/(2*-1)   =   (2 +/- sqrt(4- -60))/(-2)  = (2 +/- sqrt(64))/-2  =  (2 +/- 8)/-2. This breaks into two cases (the plus or minus).

 

(2 + -8)/-2 = -6/-2 = 3    and  (2--8)/-2 = (2+8)/-2 = 10/-2 = -5. So x =-5,3.

 

To find three points, you can just pick any values you want for x and then solve for y. For instance, if x=1 I have

y=-(1)^2 -2(1)+15 = -1-2+15 = -3+15 = 12. So (1,12) is a point on the graph.