Rewrite the function in standard form, intercept form, find the vertex, find the y-intercept, and find the x-intercepts. show your work f(x)=(x+3)^2-4

We have the function,

On simplifying, we get,

i.e.

Thus, the standard form of the function is .

Now, the factors of the given functions are (x+1) and (x+5).

Since, the intercept form of the function is the factored form of the function.

So, we have, intercept form of the function is .

Now, we know that,

Value of x-coordinate of the vertex is i.e. i.e. i.e. x= -3

Then, i.e. i.e. f(-3)=-4

So, the vertex of the function is (-3,-4).

Further, we know that, 'the y-intercept of a function is the point where the function crosses y-axis'.

So, when x=0, we have, i.e. f(0) = 5

Thus, the y-intercept is (0,5)

Also, 'the x-intercept of a function is the point where the function crossese x-axis'.

Then, for f(x)=0, we have i.e. i.e. x= -1 and x= -5

Thus, the x-intercept are (-1,0) and (-5,0).

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