CPhill

y ( y + 5)           distribute the y over the terms in the parentheses

y * y  +   y * 5  =

y^2  +  5y

Yep...last choice.....

Correct  !!!!!

For the  second one.....I'll use a graph  [ although I can also solve it algebraically, if you want me to ]

Look at the graph, here.....

https://www.desmos.com/calculator/sic40iw0e7

The height of the arch is ≈ 381 ft   and  the length of the bridge above the arch is ≈ 1791 ft

For the first one.....here's a hint......expand each answer.....see if the second one leads you to

y = x^2  + 4x  -  3

For the second one.....the vertex  is  (10, 60)

The seconds are on the x axis and the speed is on the y axis.....so.......

 It takes 10 seconds for the car to reach 60 mph

Look at this, NSS

In the form

ax^2  +  bx  + c

The x coordinate of the vertex   is given by    -b / [ -2a ]

So we have

-2x^2  + 8x  - 18

So......b = 8   and   a  = -2

So.......the x coordinate of the vertex  is   [ -8 ] / [ 2 * -2 ]  =  -8/-4  =  2

And the axis of symmetry has the same value  ⇒     x  =  2

We could find the y value of the function by  putting 2 back into it, but we don't have to in this case

The first answer is the only one that makes sense

All we need to do here, NSS, is to find the vertex

It appears that it is  ( 50, 150 )  =  (h, k )    

So....the form is

y =  a (x - h)^2 +  k  =  a(x - 50)^2  +  150   

Note  .... "a"  =  - 3/ 50 

So.......Your answer is correct  !!!!.....good job !!!

The first function is defined on (-inf, -1] U (1, inf )

However.........the second function  is only defined for (1, inf )

Note  that if let x = -2, the first function is

sqrt   ( [-2 + 1 ] / [ -2 -1] )  =  sqrt ( -1 / -3 )  =  sqrt (1/3)

But....in the second function we have

sqrt  [ -2 + 1 ]  / sqrt [ -2  - 1 ]  =  sqrt [ -1] / sqrt [ -3]  and the numerator/denominator are both non-real

Check your screen size.....if it's too large, it will "cut off"  these functions.......

Im using Google Chrome set at 125%.....the functions show up just fine, for me.....