Mathematics, 17.07.2019 20:00 dxnimxriee

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.

Answers: 1

Show answers

Answers

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.

Answer from: taheraitaldezign

The given graphs show functions that have been transformed from the quadratic parent, f(x) = $\rm x^2$ and this can be sketched by using the rules of transformation.

Given :

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

1) The graph of g(x) --

The graph of the function g(x) can be sketched by translating the graph of the parent function f(x) downwards by a factor of 3 and then translating that graph by a factor of 3 in the left direction. The resulting graph is the graph of g(x) which is given by:

$\rm g(x) = (x+3)^3-3$

2) The graph of h(x) --

The graph of the function h(x) can be sketched by taking the image of the parent function f(x) about the y-axis and then stretching that graph vertically by 3 units. The resulting graph is the graph of h(x) which is given by:

$\rm h(x) = -3(x)^2$

3) The graph of d(x) --

The graph of the function d(x) can be sketched by translating the graph of the parent function f(x) downwards by a factor of 3 and then translating that graph by a factor of 3 in the right direction. The resulting graph is the graph of d(x) which is given by:

$\rm d(x) = (x-3)^3-3$

For more information, refer to the link given below:

link

Answer from: Quest

step-by-step explanation:

Based on the results of the simulation is there statistical evidence that the spinner is not fair

Answer from: Quest

solution:

the given function is ,

$f(x) = 4 x^3 - 72 x^2 + 320 x,$

= $4x( x^2- 18 x + 80)\\\\ 4 x(x^2-10 x -8 x + 80) \\\\ 4 x[(x-10)(x-8)]$

the three roots of this quadratic function is , 0 ,8 and 10.all the roots are real and rational.

if a quadratic equation is of the form ,

$f(x) = a x^3+ b x^2 + c x+d,$

sum of the roots = a + b +c= 0+8+10=18= $\frac{-b}{a}$

product of roots taken two at a time = a b + b c+ c a = 0+80+0=80 = $\frac{c}{a}$

product of roots = a b c = 0= $\frac{d}{a}$

there are 11 doors in a hall starting from 0 to 11.the entry in the hall is permitted through gate number 0 and exit is allowed through only gate number 8 and 10.so, three roots(0,8,10) of quadratic function $f(x) = 4 x^3 - 72 x^2 + 320 x,$ is given by entry and exit route of this hall.