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.

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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:

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

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Answer from: Quest

At a constant it will take one hour to travel 32 mi.at that speed it will take 1/2 hr to travel the remaining 16 mi.it will take 1+1/2 hr to travel the 48mi @ 32mph.so 1 hr = 60 min& 1/2 hr = 30 min1+1/2 hr = 90 min.there are 60s in each 90 × 60 = 3600 seconds.the real question seriously is he why are they driving so slow? ! lol.

Answer from: Quest

answer is 8x+24

area of vanessa's patio = length × width

given, length = (3x² + 5x + 10)

width = (x² - 3x - 1)

area of vanessa's patio = (3x² + 5x + 10)(x² - 3x - 1)

= 3x²(x² - 3x - 1) + 5x(x² - 3x - 1) + 10(x² - 3x - 1)

= 3x⁴ - 9x³ - 3x² + 5x³ - 15x² - 5x + 10x² - 30x - 10

= 3x⁴ - 4x³ - 8x² - 35x - 10

hence, expression of vanessa's patio = (3x⁴ - 4x³ - 8x² - 35x - 10)

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The given graphs show functions which have been transformed from the quadratic parent, f(x) = x2. de...