Question

What are the coordinates of the x-intercept(s) of the graph of y = (x - 6)(x + 5)?

Answer 1

Ok, let me help you step by step. When you have a point that is an x-intercept, what is the y value for that point?

Answer 2

ummm would it be 0? i dont know im not good in algebra

Answer 3

Exactly, good job :). Now that we know that \(y\) should be zero, lets substitute that into the equation
\(y = (x - 6)(x + 5)\)
\(0 = (x - 6)(x + 5)\)

Now, you know that between the brackets there is a hidden multiply sign, right? They don't write it so it looks neater, but there is a multiply sign there
\(0 = (x - 6)(x + 5)\)
\(0 = (x - 6)\times(x + 5)\)

Now here is a clue. You see that in this equation, where one thing (x-6) times another thing (x+5) is equal to 0? Therefore, one of those numbers, either (x-6) or (x+5) is equal to 0. You might ask why? Think about this

What is \(5\times0\) equal? 0
What is \(0\times5\) equal? 0
What is \(62382\times0\) equal? 0
What is \(0\times693247284729430\) Equal? 0

Everytime a number becomes times with 0, it ends up being zero. Therefore, since we know that since \((x - 6)\) times \((x + 5)\) equals 0, one (or both) has to be zero. Does that make sense?

Answer 4

Please reply if that makes sense, so I can give you the answer ;)

Answer 5

it kinda makes sense

Answer 6

What makes it that you don't fully understand? Just say so

Answer 7

it just all the things we do my teacher teaches something easy and i actually understand it but then she add alot of other stuff and i get lost but i just dont really understand any of it like i got lost at heres a clue thats where you lost me

Answer 8

Ah, so you got lost in that bit. Lets make another fake equation, so I can explain better
Imagine this equation:
\[0=x\times y\]Now, we can see that when we multiply both these numbers, we get 0. That gives us a hint. Whenever two (or more) numbers multiply each other becomes 0, then one of them must be 0.

As said before, this is always the case. You might have a huge equation multiplying each other, but if there is a 0, it will always be a zero
\[634*63267*6711*85*24532*76547*0=0\]
That huge lines becomes zero, because it multiplies with a 0. Same thing in the equation \(0=x×y\). Either \(x\) or \(y\) is equal to 0. This is because when any number times 0, it will become zero. That is simply a fact you got to remember.

Here is one way of putting it:
\(\text{If the product of any two numbers is zero, then one or both of the numbers is equal to
}\)\(\text{zero.
In other words, if x times y becomes 0, then x must be 0, or y must be 0}\)

Thats just simply something to remember. Does it make sense now?

Answer 9

so x and y would be 0?

Answer 10

In \(0=x\times y\), exactly :). But we have a different equation, \(y = (x - 6)(x + 5)\)

Now, since we know we are looking for the x-intercept, we know that the \(y\) value is equal to 0, so lets do that
\(y = (x - 6)(x + 5)\)
\(0 = (x - 6)(x + 5)\)
Now, from what we learned before, that is the same as
\(0 = (x - 6)\times(x + 5)\)

Now, since when we multiply it becomes 0, one (or both) have to be zero. So lets do that for each one.

Lets do \((x-6)\) first
\((x-6)\) could be zero, so
\((x-6)=0\)

Remove the brackets
\(x-6=0\)
\(x=6\)
Thats one of the x-intercept, 6

Lets do \((x+5)\) second
\((x+5)\) could be zero, so
\((x+5)=0\)

Remove the brackets
\(x+5=0\)
\(x=-5\)
Thats the second x-intercept, -5

So, the two \(x-intercepts\) are 6 and -5. Hope that makes sense @breannabusby :)

Answer 11

it actually does...thanks

Answer 12

No problem :D

Answer 13

is this stuff easy for you?

Answer 14

For me, yeah. As you do them again and again, you start to get a hang of it and understand how to do it easily. Don't worry, you will get it eventually, I promise :)

Answer 15

what grade are you in