Question

Why can 25x^2 + 144 not be rewritten as a group of factors?

Answer 1

@hartnn do you think you can help me again :)

Answer 2

ok, a quadratic expression ax^2+bx+c can be factored if b^2-4ac is a perfect square.

Answer 3

so, compare 25x^2+144 with ax^2+bx+c and tell me what u get for a,b,c ?

Answer 4

ok, 'a' would be 25 and 'c' would be 144 but i don't have a 'b'

Answer 5

b=0

Answer 6

yup, 25x^2+144= 25x^2+0x+144

Answer 7

so, now whats b^2-4ac = ...?

Answer 8

so then is would be 0 - 4 (25)(144) = -14,400?

Answer 9

is that a perfect square?

Answer 10

no because it is negative right? so would that be my reason?

Answer 11

correct!
since the discriminant b^2-4ac for 25x^2+144 is NOT a perfect square, it cannot be factored into groups. :)

Answer 12

ok :) thank you very much! but do you think you can help me with one more? it is a bit bigger?

Answer 13

sure!

Answer 14

Ok :) so with the same equation, 25x^2 + 144, i have to graph it on a graph. So far i have put it on a graph and it is a positive parabola that is very narrow, other then that i have points the i solved for as well which are (-2, 244), (-1, 169), (0,144), (1,169), and (2, 244). Now i am asked to find the average rate of change and whether it is increasing or decreasing, from left to right. And i also have to justify my observation with calculations.
So far i know kind of that you are suppose to have two points (or something around those lines) and find the slope of them. That way i would have to rate of change but i don't know how to solve for the rest...

Answer 15

i am very sorry how long it is :(

Answer 16

do you think you can help @hartnn ? i know its a lot and im sorry :(

Answer 17

oh, sorry for the late reply! i got busy with these reports...

increasing if avg. rate of change (or slope) is positive
decreasing if avg. rate of change (or slope) is negative

Answer 18

That's it? what about the left to right thing? and what about calculations?

Answer 19

also what would be my two points that i would use?

Answer 20

ok, from graph you would observe that it is decreasing from left to right till x=0 and then increasing thereafter.

so, first take 2 points on left of x=0
show that slope is negative (calculations part)

Answer 21

then take 2 points on right of x=0
show that slope is positive , hence increasing

Answer 22

Ahh is that all i need?

Answer 23

i think yes. that would cover up all questions...

Answer 24

thank you very very much ! :D

Answer 25

observations will be from graph and calculations is of finding slope with the formula.
welcome ^_^