SOLUTION: 1. Consider the family of parabolas given by y=-x^2-10x+c a) Sketch 3 distinct members of this family of parabolas such that there are 2, 1 and zero x intercepts. b) Determi

Algebra ->  Graphs -> SOLUTION: 1. Consider the family of parabolas given by y=-x^2-10x+c a) Sketch 3 distinct members of this family of parabolas such that there are 2, 1 and zero x intercepts. b) Determi      Log On


   

Question 1014734: 1. Consider the family of parabolas given by y=-x^2-10x+c
a)
Sketch 3 distinct members of this family of parabolas such that there are 2, 1 and zero x intercepts.
b)
Determine the number of x intercepts in terms of the parameter c.

Answer by Fombitz(32388) About Me  (Show Source):
You can put this solution on YOUR website!
.
Use the determinant.
D=b%5E2-4ac=%28-10%29%5E2-4%28-1%29%28c%29=100%2B4c
For 2 roots, D%3E0
100%2B4c%3E0
c%3E-25
For 1 root, D=0
c=-25
For no roots,D%3C0
c%3C-25