how do i arrange this quadratic equation so i can determine if the parabola is up or down?

Question

best step by step gets 10 points

-6 + x^2 - 5x
so how would u arrange it so it would be like
ax^2 + bx+ c??? and not

-c + ax^2 - b
thanks

Answer 1

rearrange terms in quad function order
x^2-5x-6


if the "a" value...in this case 1...is positive, parabola opens upward
if the a value is negative, the curve opens downward..

Answer 2

You don't really have to rearrange it, you can just look at the coefficient of x^2. Positive "a," it points up (i.e., has a minimum and increases in both directions away from the minimum). You don't really have to do anything else.

Though I'm assuming that you have a "y =" that is implied but omitted:

y = -6 + x^2 - 5x

In this case the coefficient of x^2 is positive 1, so this parabola points up (looks like 'U').

You could reorder the terms (remember, addition is commutative), but it doesn't change much:

y = x^2 - 5x - 6

... traditionally the terms are ordered by decreasing degree of x.

Answer 3

+ x^2 is U shaped
- x^2 is n shaped

-6 + x^2 - 5x =>+ x^2
1x^2 -5x-6 = ax^2 + bx+ c