Let f(x)=25x2−2 . the function g(x) is a vertical stretch of f(x) by a factor of 2. what is the equation of g(x)?

 The required equation of g(x) is

Step-by-step explanation:   The given function is

The function g(x) is a vertical stretch of f(x) by a factor of 2.

We are to find the equation of g(x).

Since the co-efficient of x² in equation (i) is positive, so the parabola opens upward.

So, the vertical stretch will be in the downward direction.

Since g(x) is the vertical stretch of f(x) by 2, so we must have

Thus, the required equation of g(x) is

there are lots of ways.   pick's theorem tells us if the vertices are lattice points the area a is

a = b/2 + i - 1

where b is the number of boundary lattice points and i is the number of interior lattice points.

in the figure i count b=16, i=50 so

a = 8 + 50 - 1 = 57

let's try the shoelace formula.   the area is half the sum of the cross products of the sides.  

a(-2,6)   -2(2)-6(-5) = 26

b(-5,2)   -5(-3) - 2(-2) = 19

c(-2,-3) -2(-3) - (-3)(4) = 18

d(4,-3)   4(3) - (-3)(5) = 27

e(5,3)   5(3) - 3(1) = 12

f(1,3)     1(6) - 3(-2) = 12

a(-2,6)

each of the cross products is twice the area of the triangle with the associated side and one vertex the origin. so the area of abo=26/2=13.

area = (1/2) (26 + 19 +   18 + 27 + 12 + 12) = 57

that checks!

1) c 2143.6 cm

2) c 113.0 m

3) a 33.5 ft

4)   d 2 cm

5) c 20 mm

6) 180 in

7) d 120 ft