is there a way to find the exact x intercepts for y = (x^2) - 2?

Question

its close to 1.4 but apparantly there is a way to get an exact anwer with radicals. could you show me how please?

Answer 1

I take it that by "x intercepts" you mean "the intercepts on the x-axis," i.e. for y = 0. (Just put y = 0 in the equation and solve x^2 = 2, so that the right-hand side of your equation becomes 0 also.)

There will then be two intercepts, at +/- sqrt 2 where, because of font limitations, *** I use "sqrt" for the radical sign "square root of."

These rooots can also be written as +/- 2^(1/2) or 2^(0.5).

The numerical value of sqrt 2 is 1.41421356....

This number never ends, goes on and on without any sustained repeating pattern, and so can never be expressed "exactly" in terms of simply continuing to write out further digits. The use of sqrt, the radical sign, etc. is the best that you can do.

It is an "irrational number," the first such number shown by the Greeks to NOT be expressible as a fractional expression in terms of pure integers.

I hope this helps.

Live long and prosper.

*** NOTE ADDED: I found the radical sign in a "Symbol table": √. So, the two intercepts are most compactly written as +/- √2.

Answer 2

Hmm... besides to be frank. there heavily is not any gradient for this line Gradient of the line = (2-2)/(-5-8) = 0/-13 The gradient would be 0. subsequently it won't hit the y axis and subsequently, no y intercepts. yet as an occasion, i supply you 2 coordinates (2,4) and (5,8). The gradient would be (8-4)/ (5-2) = 4/3 subsequently, employing linear equation : y = 4/3x + c (c is the y interception) subsequently, employing between the coordinates, replace y = 2 and x = 4 into the equation subsequently, 2 = sixteen/3 + c c (y intercept) = 2 - sixteen/3 = - 10/3 subsequently the equation of the line : y = 4/3x - 10/3

Answer 3

The short answer to your question is no. The reason behind it is because the x-intercepts would be irrational. Irrational numbers are, by definition, numbers that neither terminate nor repeat.

0 = x^2 - 2
x^2 = 2
x = +/- sqrt(2)

From an algebraic standpoint, expressing the x intercepts as sqrt(2) and -sqrt(2) is as exact as you're going to get.

From a numerical standpoint, there's absolutely no way to get the exact x-intercepts. Any other answer you get, even the one given to you on your calculator, would be wrong.

Answer 4

The x intercept is where y = 0

So 0 = x^2 - 2
Add 2 to both sides,
and then x ^2 = 2

Take the square root (PLUS OR MINUS!!!) of both sides and you're done!