Rewrite the function in standard form, intercept form, find the vertex, find the y-intercept, and find the x-intercepts. show your work y=(x-1)^2-9

The function is given as

We will simplify the function,

i.e.  gives

Therefore, the standard form is given by .

As, the given functions have factors (x-4) and (x+2).

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

Thus, the intercept form is .

Now, it is known that,

X-coordinate of the vertex is i.e. i.e. i.e. x= 1

So, the value of y at x=1 is, i.e. i.e. y= -9

Thus, the vertex of the given function is (1,-9).

Since, 'the y-intercept of a function is the point where the function crosses y-axis'.

At x=0, we have, i.e. y= -8

Therefore, the y-intercept is (0,-8)

And, 'the x-intercept of a function is the point where the function crosses x-axis'.

So, for y=0, we have i.e. i.e. x= 4 and x= -2.

Thus, the x-intercept are (4,0) and (-2,0).

b. 1.25 hr

step-by-step explanation:

if you have a constant speed of 60 mph, then you have a ratio between 60 mi. to 1 hr. dividing both sides by 60 we get the ratio

1 mi. to

then mult. both sides by 75 we get the ratio

75 mi. to

simplifying we get

75 mi. to

or 1.25 hr.