Question

Which transformations have been applied to the graph of f(x) = x2 to produce the graph of g(x) = –5x2 + 100x – 450? Select three options. The graph of f(x) = x2 is shifted down 50 units. The graph of f(x) = x2 is shifted up 50 units. The graph of f(x) = x2 is shifted left 10 units. The graph of f(x) = x2 is shifted right 10 units. The graph of f(x) = x2 is reflected over the x-axis.

Answer 1

B D E

Explanation:

I took the test on edge

Answer 2

The graph of f(x) is shifted up 50 units

The graph of f(x) is shifted right 10 units

The graph of f(x) is reflected over the x-axis

Explanation:

we have

`f(x)=x^(2)`

This is a vertical parabola open upward

The vertex is a minimum

The vertex is the origin (0,0)

`g(x)=-5x^(2)+100x-450`

This is a vertical parabola open downward

The vertex is a maximum

The first thing to note is that fx) is a parabola that opens up and g(x) opens down, so a reflection across the x-axis must have been applied.

Find the vertex of g(x)

Convert to vertex form

`g(x)=-5x^(2)+100x-450`

Complete the square

`g(x)=-5(x^(2)-20x)-450`

`g(x)=-5(x^(2)-20x+100)-450+500`

`g(x)=-5(x^(2)-20x+100)+50`

`g(x)=-5(x-10)^(2)+50`

The vertex is the point (10,50)

so

To translate the vertex of (0,0) to (10,50)

The rule of the translation is

(x,y) ------> (x+10,y+50)

That means ----> The translation is 10 units at right and 50 units up

therefore

The transformations are

The graph of f(x) is shifted up 50 units

The graph of f(x) is shifted right 10 units

The graph of f(x) is reflected over the x-axis