Howdy Clemintine, & I sure hope all is well. :)
As for your question,
To determine the X-intercepts of a function, you set the function equal to 0. In this case, we have:
F(X) = 4X^2 -- 28
F(X) = 0 ==>
4X^2 -- 28 = 0
To solve for X requires that it be isolated, freed from all operations being performed on it. That means:
We need to remove the coefficient. (In this case, the coefficient is the 4 being multiplied by the X^2 term.)
We need to remove any exponents the X-term is being raised to. (In this case, X is being raised to the power of 2.)
& we need to make positive if it were negative, i.e. turn -- X into X. (In this case, X is already positive).
So we begin by adding 28 to both sides of the equation. We get:
(Note: We need to add 28 to both sides, so as to maintain the equality, much as you'd need to add the same amount of weight to both sides of a scale to keep it level. An equation is no different.)
4X^2 -- 28 + 28 = 0 + 28
Simplifying yields:
4X^2 = 28
Next, we divide both sides of the equation by 4. We get:
4X^2/4 = 28/4
Simplifying yields:
X^2 = 7
Finally, we take the square root of both sides of the equation, by raising them to the power of 1/2. We get:
(X^2)^(1/2) = 7^(1/2)
Simplifying yields:
X = +/-- 7^(1/2) (approximately) = +/-- 2.64575
(Note: +/-- means + or --. It is necessary to include & consider both roots, since both are valid, & both would yield 7. If you were to plug in -- 2 into your calculator & square it, you'd get 4, just as if you'd plugged in 2.)
Therefore, the X-intercepts of F(X) = 4X^2 -- 28 are -- 7^(1/2) (or -- 2.64575) & 7^(1/2) (or 2.64575).
I sure hope that was clear & helpful enough. :) Good luck, take care, & have a great day. :)
Cheers! :)
參考: What I learned in High School Math, especially Calculus.
The x-intercepts are the values of x for which f(x) is zero.
So,
0 = 4x^2-28
0 = x^2 -7
x^2 = 7
x = + sqrt(7) and - sqrt(7)
sqrt(7) is 2.65
so the x-intercepts are (2.65,0) and (-2.65,0)