Number 4

i. Find coordinates of point P

if know one of axes let's call it the q axis is -2

then cut off the other axis / the p axis is :

y = (X+2)(X-5)

q = ( X1 + 2 ) = 0

q = X1 = -2

then :

p = ( X2 - 5 ) = 0

p = X2 = 5

then the p axis is 5

ii. find the equation of line of symmetry

X symmetry = X1+X2 / 2 or q+p / 2

X symmetry = -2+5 / 2

X symmetry = 3/2

X Symmetry = 1,5

then the X.symmetry is 3/2 or 1,5

iii. find the maximum / minimum value

find maximum/minimum value :

y = f(x) = (X+2)(X-5)

y = f(x) = X²-5X+2X-10

y = f(x) = X²-3X-10

input x symmetry to f(x) :

x symmetry is 3/2

then:

y = f(3/2) = (3/2)²-3(3/2)-10

y = 9/4 - 9/2 - 10

y = 9/4 - 18/4 - 40/4

y = -9/4-40/4

y = -49/4

y = -12,25

then minimum value is -49/4 or -12,25

--------------------------

number 5

if scale 1:500 the area is 100cm²

then:

side length : √100

side length : 10cm

side length in scale :

1 : 500 = 10cm

1 : 200 = X

scale comparisons :

1 : 500 / 1 : 200 = 10/X

500/200 = 10/X

5/2 = 10/X

5X = 20

X = 4cm

then side length if scale is 1:200 :

1 : 200 = 4cm

then Area if scale is 1:200 :

4² = 16cm²