Question

okay, I struggle hard core with these and I don't know why. so I need to put 0=6^2p+5p+1 into intercept form

Answer 1

slope intercept of\[0=6^2p+5p+1\]are you sure you typed it right?

Answer 2

try changing all the p's into x's if you see it better that way.

Answer 3

oh no! i meant for the p to be squared!

Answer 4

it should be 6p^2+5p+1=0 and i need to change that into x-intercept form

Answer 5

find the x-intercepts you mean then, so solve the equation

Answer 6

I'm not allowed to use the quadratic formula. i can only factor it

Answer 7

6p^2+5p+1=0
( _p + _ )( _p + _ )=0
we need to fill in the blanks such that the last terms multiply to 1 and the first terms multiply to 6

Answer 8

okayyy and how do i find those solutions mathmatically?

Answer 9

what are the only two integers that can multiply to be 1 ?

Answer 10

1 aaand 1 of course

Answer 11

or -1 and -1

Answer 12

good observation that it could be negative, but since everything is postive here we will just assume it is positive for now
(_p+1)(_p+1)
what pairs of integers multiply to 6 ?

Answer 13

1 & 6
2&3
aanndd thats it

Answer 14

right, and since we know that
(3p+1)(2p+1)=0
that implies that either 3p+1=0 or 2p+1=0, or both
so solve those two equations and you get your two values of x for which y is zero, i.e. where the graph intercepts the x-axis.

Answer 15

so (3p+1)(2p+1)=0 is tha answer? and i can use this process for every problem?

Answer 16

you should always double-check that you get the correct cross term to be sure you have done it right
(3p+1)(2p+1)=0
6p^2+3p+2p+1=0
6p^2+5p+1=0
^^
cross term
when factoring something that looks like ax^2+bx+c=0
sometimes you can find numbers that multiply to a and c, but do not produce the correct b, so you should FOIL out what you have to be sure

also, you are not done with the statement (3p+1)(2p+1)=0
you still need to follow what I said above and solve for p:

since we know that
(3p+1)(2p+1)=0
that implies that either 3p+1=0, or 2p+1=0, or both equal zero
so solve those two equations and you get your two values of x for which y is zero, i.e. where the graph intercepts the x-axis.

Answer 17

dude, how I wish you were my math teacher

Answer 18

hehe, I do too sometimes
welcome!

Answer 19

oh, typo...
should say:
so solve those two equations and you get your two values of p for which the function is zero, i.e. where the graph intercepts the p-axis.

Answer 20

haha, yes i understand! thank you so much!