Question

Consider the equation: x2 − y2 = 9. Find the x- and y-intercept(s) of the graph, if any exist. (If an answer does not exist, enter DNE.)
x-intercept (x, y) = ____ (smaller x-value)
x-intercept (x, y) =____ (larger x-value)

Answer 1

For finding any intercept of any function/equation
Just put x=0 for finding y intercept.
Put y=0 for x-intercept....

Answer 2

so would it be (-9,0) for the smaller x-value and (9,0) for the larger x value?

Answer 3

If you plug in y=0, what do you get for x?

Answer 4

9?

Answer 5

How so? show your work.

Answer 6

\( x^2 − y^2 = 9\)

Put in y=0. The equation becomes...?

Answer 7

x2-0=9

Answer 8

Ok, simplify....

\(x^2 = 9\)

Now what? How do you find x from this point?

Answer 9

find the square root which is 3

Answer 10

Well, yes... you take the sq. root of both sides, and what do you need to use when you do that?

\(\sqrt{x^2} =???\sqrt{ 9}\)

You need something here on the right hand side when you take that sq root....

Answer 11

the plus and minus sign

Answer 12

Exactly....

\(\sqrt{x^2} =\pm \sqrt{ 9}\)

so your (two) solutions for x are?

Answer 13

(-3.0) (3,0)

Answer 14

yes, those are the intercepts. :)

Answer 15

You see the error you were making when you said 9 and -9?

Answer 16

yes i see it now, thank you so much :)

Answer 17

You're welcome, happy to help. :)