Mathematics: Select all the transformations of f(x) = x2 that combine to result in the graph of function g below. A parabola with vertex negative 1 comma negative 2 that opens downward. The graph passes through the points negative 3 comma negative 3 and 1 comma negative 3. Group of answer choices vertical stretch by a factor of 2 translation of 1 unit right translation of 2 units up translation of 1 unit left reflection across the x-axis horizontal stretch by a factor of 2 translation of 2 units down

Select all the transformations of f(x) = x2 that

saucyboyFredo

01.02.2022

Options 4, 5 and 7.

Step-by-step explanation:

The general function is

f(x)=x^2

The vertex form of a parabola,

g(x)=a(x-h)^2+k ...(1)

where, a is a constant and (h,k) is vertex.

It is given that vertex of a parabola is (-1,-2).

g(x)=a(x-(-1))^2+(-2)

g(x)=a(x+1)^2-2 ...(2)

It passes through (-3,-3).

-3=a(-3+1)^2-2

-3+2=4a

-1=4a

$-\dfrac{1}{4}=a$

Put this value in (2).

$g(x)=-\dfrac{1}{4}(x+1)^2-2$

Now,

h=1>0, so translation of 1 unit left.

a=-1/4<0 Reflection across the x-axis and vertical compression by factor 4.

k=-2<0, translation of 2 units down

Therefore, the correct options are 4, 5 and 7.

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