Help Identifying x-intercepts of quadratic functions

[Kalzar89]

Homework Statement

Identify the vertex and x-intercept(s) of the quadratic function algebraically.

Homework Equations

f(x) = 1/2x^2 - 4

1/2 Is the coefficient if its not clear.

The Attempt at a Solution

Ok I do not need help finding the vertex I have already got that, I need help factoring it out to find the x-intercepts.

Here is my attempt

0 = 1/2x^2 - 4
0 = 1/2 (x^2 - 8)

That is as far as I can factor it, I am terrible at factoring these and I actually have a way easier time factoring trinomials and polynomials.

Could you please explain how I am to factor farther and how am I supposed to solve for the x-intercepts after its all factored. I have even looked all over the internet for a good factoring tutorial guide but I just cannot even understand them.

Thanks

 

[AssyriaQ]

Ok I do not need help finding the vertex I have already got that, I need help factoring it out to find the x-intercepts.

Here is my attempt

0 = 1/2x^2 - 4
0 = 1/2 (x^2 - 8)

That is as far as I can factor it, I am terrible at factoring these and I actually have a way easier time factoring trinomials and polynomials.

There is no need to worry that much about factoring. You have

$$\frac{1}{2}x^{2}-4=0.$$​

Simply solve for x to obtain the intercept.

 

[HallsofIvy]

I believe that was what he was trying to do! Kalzar89, there is no need to factor.
$(1/2)x^2- 4= 0$
$(1/2)x^2= 4$
$x^2= 8$
and take the square root of both sides.
$x= \pm\sqrt{8}= \pm \sqrt{(4)(2)}= \pm 2\sqrt{2}$