Verified answer

Question 1:

Lets say you have an easy equation of line y = sinx,

A horizontal shift is when you add a real number to x like y = sin (x + 90) where x is in degrees

y = sin (x + 90) appears to shift the equation y = sinx to the LEFT of the graph by 90 degrees

y = sin (x - 90) appears to shift the equation y = sinx to the RIGHT of the graph by 90 degrees

Using another example of equation y = x

y = x + 2 is a vertical shift upwards from y = x

y = x - 2 is a vertical shift upwards from y = x

Question 2:

This method is called "completing the square"

Hard to show you here but answer is

y = (x-2)^2 - 4

so a =1 , h =2 , k = -4

1) It decreases to the point where x=5 y=-2. before increasing again. (U-shaped curve) [smiley face because it is a positive curve, *no negative signs before (x-h)^2]

where the lowest point of the curve is x= -h y= k

2) y=x^2-4x -> y= (x-2)^2 + 0

Factorize it. take out the x and divide the h by two. always. then square the whole bracket.