help pls inequalities work

[split lily]

HELP HOW DO I DO ALL OF THESE

[umbral granite]

so, first factorise the quadratic, to get (x+3)(x+2). so (x+2) is the length of one side and (x+3) is the length of the other

and then make the area they gave u in terms of x equal to the actual area

so

x^2+5x+6=42

then we wanna factorise so we can get x

so subtract 42 to make the whole thing equal to 0

so x^2+5x-36=0

factorise

what adds to give 5 and multiplies to give -36

9 and -4

so

(x+9)(x-4)

so rn we have two possible values of x

x=-9 and x=4

cant be -9 as it will give a negative length, which isnt possible

so has to be 4

and that is question 6 finished

now for question 7

y=x^2+3x-4

first

lets figure out what we need to find to plot it

1.y-intercept

2. roots(x intercept)

3. turning point

1. getting the y intercept is easy, its just the term with no x coefficient, so in this case it is -4

2. we should factorise to get the roots, what adds to give 3 and multiplies to give -4....4 and -1.
   so to factorise it we write it as (x+4)(x-1), which means our roots are x=-4 and x=1

3. you have to complete the square to find the turning point/ minimum.