Question

Can you tell which way a parabola will open up just by looking at the equation?

Answer 1

yes

Answer 2

if its y^2=4ax then on right and y^2=-4ax then on left
and if its x^2 = 4ay then upwards and if its x^2=-4ay then downwards

Answer 3

ax^2 + bx + c is also a parabola.

Answer 4

yeah i know that i am just telling the forms

Answer 5

IS " if the leading coefficient is greater than zero, the parabola opens upward, and if the leading coefficient is less than zero, the parabola opens downward." a decent answer?

Answer 6

you can look from y=ax^2+bx+c
the state if you want get max or min in the stationary point
you have to double differentiation
so y''=2a
and you know that if y''>0 is min point
and parabola is open
o if a>0 parabole is open

Answer 7

in standard form ax^2 + bx + c,

if a is positive, opens up
if a is negative, opens down

Answer 8

second derivative? stationary point? opens up if
\[a>0\] and down if
\[a<0\] oh what mtbender said sorry

Answer 9

yes, fuzzy...that answer is acceptable. :)

let's not nuke it guys ;)

Answer 10

@fuzzynips

IS " if the leading coefficient is greater than zero, the parabola opens upward, and if the leading coefficient is less than zero, the parabola opens downward." a decent answer?

Works for me (the sideways one is just a twist).

Answer 11

y = x^2 is a 'U'
y = -x^2 is an 'upside down U'