Question

The given graphs show functions which have been transformed from the quadratic parent, f(x) = x2. Determine which transformations were applied to the quadratic parent function to result in each graph.

Answer 1

The tansformations of were applied to the quadratic parent function to result in each graph are g(x), h(x) and d(x) with translation

Further explanation

Transformations definition is it involved by taking a preimage and transforming it in some way to produce an image.

Mathematical transformations have four main types: translation, rotation, reflection and dilation

1. Rotation is done by rotating an object about a fixed point without changing its size or shape
2. Translation is done by moving an object in space without changing its size, shape or orientation
3. Dilation is done by expanding or contracting an object without changing its shape or orientation
4. Reflection is done by flipping an object across a line without changing its size or shape

The given graphs show functions which have been transformed from the quadratic parent, $f(x) = x^2$

Which transformations were applied to the quadratic parent function to result in each graph?

Quadratic parent: $f(x)=x^2$

The graph is a parabola with $V=(0,0)$ at the origin

If $x=1$ then $f(1)=1^2 = 1$

Vertical shift means shifting in y axis. Whereas horizontal shift means shifting in x axis. Shift down means go to lower value of axis, whereas shift left goes to higher value of axis

For $g(x)$: vertical shift down 3 and horizontal shift left 3  

For $h(x)$: reflection across the x-axis and vertical strecht of 3

For $d(x)$: vertical shift down 3 and horizontal shift right 3

Learn more

1. Learn more about transformations brainly.com/question/8388091
2. Learn more about the quadratic parent function brainly.com/question/9722690
3. Learn more   about functions brainly.com/question/10904281

Answer details

Grade:    5

Subject:  Math

Chapter:   the quadratic parent function

Keywords: the quadratic parent function, transformations, graph, functions,  quadratic

Answer 2

Answers:

           g(x)                                    h(x)                                     d(x)
vertical shift down 3     reflection across the x-axis     vertical shift down 3
horizontal shift left 3     vertical strecht of 3                 horizontal shift right 3


Quadratic parent: f(x)=x^2
The graph is a parabola with vertex V=(0,0) at the origin and opens up.
When x=1→f(1)=1^2→f(1)=1

1) g(x)
The graph opens up, then there is not a reflection across the x-axis.
The vertex is at the point (-3,-3): 3 units to the left and 3 units down of the vertex of the parent funtion.
When x is 1 unit to the right from the vertex g(x)=1
Then the transformations were applied to the cuadratic parent function are:
1.1) vertical shift down 3.
1.2) horizontal shift left 3.

2) h(x)
The graph opens down, then there is a reflection across the x-axis.
The vertex is at the origin (0,0).
When x is 1 unit to the right from the vertex h(x)=-3
Then the transformations were applied to the cuadratic parent function are:
2.1) reflection across the x-axis.
2.2) vertical strecht of 3.

3) d(x)
The graph opens up, then there is not a reflection across the x-axis.
The vertex is at the point (3,-3): 3 units to the right and 3 units down of the vertex of the parent funtion.
When x is 1 unit to the right from the vertex d(x)=1
Then the transformations were applied to the cuadratic parent function are:
3.1) vertical shift down 3.
3.2) horizontal shift right 3.