Write a function in any form that would match the graph shown below.

f(x) = -2(x + 5)²(x - 2)²

Step-by-step explanation:

Let the function shown by the graph is,

f(x) =

Here, x = a and b are the zeros of the function

p and q are the multiplicity of the function.

If the graph crosses x-axis at a zero x = a, p (multiplicity) will be odd.

If the graph just touches the x-axis at x = b, q will be even.

From the graph attached,

Zeros → x = -5, 2

Graph touches the x-axis, representing the even multiplicity.

Therefore, function will be,

f(x) = k(x + 5)²(x - 2)²

y-intercept from the graph → (0, -200)

From the given function,

-200 = k(0 + 5)²(0 - 2)²

-200 = 100k

k = -2

Therefore, function represented by the graph is,

f(x) = -2(x + 5)²(x - 2)²

x is variable or an unknown value to find

example:

2x = 5 which means x = 3

g = (2, 2)

step-by-step explanation:

given the ratio is 1 : 1 then f is the midpoint of eg

let the coordinates of g = (x, y)

using the midpoint formula

(0 + x) = 1 ( multiply both sides by 2 )

0 + x = 2 ⇒ x = 2

similarly

(4 + y) = 3 ( multiply both sides by 2 )

4 + y = 6 ( subtract 4 from both sides )

y = 2

coordinates of g = (2, 2)