Need writing a quadratic equation from a function given the graph, screenshot posted of the question

g(x) = -x² + 10x - 30

the equation of a quadratic in vertex form is

y = a(x - h)² + k

where (h, k ) are the coordinates of the vertex and a is a multiplier

here vertex = (5, - 5 ), hence

y = a(x - 5)² - 5

to find a substitute the point on the graph (8, - 14) into the equation

- 14 = 9a - 5 ⇒ 9a = - 9 ⇒ a = - 1

y = - (x - 5)² - 5 = - (x² - 10x + 25) - 5 = - x² + 10x - 30

g(x) = - x² + 10x - 30 ← in standard form

given that triangle abc is transformed two times to get triangle

a"b"c"

first abc is transformed in to a'b'c' as follows:

the coordinates of a are (1,-1) and transformed into a'(-1,1)

similarly b (4,-2) became b'(-4,2) and

c(7,-2) became c'(-7,2)

i.e. (x,y) becomes (-x,-y)

this is nothing but reflection about a point here origin.

thus first transformation is reflection on the origin.

next is exactly shifting 3 units down

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