I used three different equations to generate these graphs?
Can anyone work out what i could have typed?
Any parabola with vertical axis is of the form $y= a(x- x_0)^+ y_0$. A parabola with horizontal axis is of the form $x= a(y- y_0)^2+ x_0$. A parabola with axis that is neither horizontal nor vertical can be derived from those through a rotation.
Any conic section (parabola, ellipse, circle, hyperbola) has equation of the form $Ax^2+ Bxy+ Cy^2+ Dx+ Ey+ F= 0$. The conic section is a parabola if and only if $B^2- 4AC= 0$
(Except for "degenerate cases" which reduce to a single line or two parallel lines. For example if A= C= 1, B= 2, D= E= F= 0 that formula is $x^2+ 2xy+ y^2= (x+ y)^2= 0$ which is true for y= -x, a single line.If A= C= 1, B= 2. D= E= 1, F= 0, the equation is $x^2+2xy+ y^2+ z+ y= (x+ y)^2+ (x+ y)= (x+ y)(x+ y+ 1)= 0$, the parallel lines y= -x an y= -x- 1.)