Question

How do you find the discriminant and how many solutions does `x^2 + 8x + 16 = 0` have?

Answer 1

Equations of the form `Ax^2+Bx+C=0`

Discriminant=`D=sqrt(B^2-4AC)=8^2-4*1*16=0`
which means there is one solution
For `D>0` there would be two solutions,
for `D<0` there would be no (real) solution.

Without working out the discriminant, it's fairly easy to see that:
`->(x+4)^2=0->x=-4`
In the graph you see the standard `x^2`-graph moved by `-4`
graph{x^2+8x+16 [-15.5, 4.5, -2.4, 7.6]}