When you have a bunch like this, I find it easiest to graph them.
The numbers of real solutions are ...
2
0
2
1
I know you know how to use Desmos to graph these. You can also write a little spreadsheet program to compute the discriminant b^2 -4ac, or do it the hard way.
1^2 -4(-3)(12) = 145 . . . positive, so 2 solutions
(-6)^2 -4(2)(5) = -4 . . .. negative, so 0 solutions
7^2 -4(1)(-11) = 93 . . . .. positive, so 2 solutions
(-8)^2 -4(-1)(-16) = 0 . .. zero, so 1 solution
Answer:
y=(x-2)²+2
Step-by-step explanation:
y=x²-4x+6 (a=1 , b=-4 , c=4)
vertex form : y=a(x-h)²+k
h and k are the vertex coordinate :
h=-b/2a =-4/-2
h=2
find f(2) to find k in the equation :x²-4x+6
(2)²-4(2)+6
4-8+6=2 (k=2)
vertex form : y=a(x-h)²+k (a=1)
y=(x-2)²+2
180/3=60
60=3x-12
72=3x
X=24
The answer is X=3 or x=5/3