Question

Ax^2 + Dx + Ey + F = 0; A doesn't equal 0
is a vertical line if D^2=4AF and E=0

i need points to graph

Answer 1

If E is zero, this is a quadratic equation. D^2 = 4AF indicates there is only one solution.

Answer 2

That solution will be x = -D/2A.

Answer 3

okay so put in the quadratic equation thing

Answer 4

how did you get that

Answer 5

Facts to remember about this problem:

\[ax^2+bx+c=0 \implies x=\frac{-b \pm \sqrt{b^2-4ac}}{2a}\]
Note that the conditions given in the problem make the discriminant (the argument of the square root in the fomula) zero.

Answer 6

Got it?

Answer 7

so do D=2 square root AF

Answer 8

I suppose x=-b/2a could be considered a vertical line in the Cartesian plane, but it is usually thought of as a point on the real line.

Answer 9

ohhhhh nevermind i got it

Answer 10

Do math every day.

Answer 11

so if D^2 > 4AF what happens

Answer 12

Then there are two distinct, real-number solutions.

Answer 13

You can get them from the quadratic formula.

Answer 14

ok i see

Answer 15

what is D^2 < 4AF

Answer 16

@AnimalAin

Answer 17

In that case, there is no real-number solution. The two solutions are complex-conjugates of the form a +bi and a - bi.