What are the x-intercepts of: f(x)=4x^2-28?

4x^2-28=0
x^2=7
x=\/'''''7'''' & - \/''''7'''''
or x=2.64575 & -2.64575

f(x) = 4x^2 - 28
y = 4x^2 - 28

Let y = 0 and solve for x:
y = 4x^2 - 28
0 = 4x^2 - 28
4x^2 = 28
x^2 = 7
x = ±√7

For y = x^2 - 3x - 28, set y = 0 and clean up for x to get the x-intercepts. 0 = x^2 - 3x - 28 0 = (x - 7)(x + 4) x - 7 = 0 or x + 4 = 0 x = 7 or x = -4 x-intercepts are -4 and seven.

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! :)

factor out 4 and set it equal to 0
4(x^2-7)=0
divide each side by 4
x^2-7=0
move the 7 to the other side
x^2=7
square root each side
x=+/-sqrt(7)
remember it's plus or minus sqrt(7) because you're taking the square root

+ or - sq.rt. of 7

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)