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I am confused on this problem and am looking for help. If anyone could help me it would be appreciated

I am confused on this problem and am looking for help. If anyone could help me it-example-1
User Marandil
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1 Answer

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Answer


g(x)=-2(x+5)^(2)-3

0. Horizontal translation 5 units.

,

1. Reflection over the x-axis

,

2. Vertical compression 2 units

,

3. Vertical translation down 3 units


y=-(x+5)^2

Step-by-step explanation

• Writing the function in completed-square form.

As a ≠ 1, where a is the coefficient of the leading term, to write it in the completed-square form we have to make a = 1:


g(x)=-2x^2-20x-53
g(x)=-2(x^2+10x+(53)/(2))

Now we have to take half of the x term and square it and add it to the function as follows:


(10)/(2)^2=5^2=25
g(x)=-2((x^2+10x+25)+(53)/(2)-25)

Finally, we have a Perfect Squared Trinomial in the left side that we can rewrite as follows, obtaining our function g(x):


g(x)=-2(x+5)^2+(3\cdot-2)/(2)
g(x)=-2(x+5)^2-3

As our parent function is:


f(x)=x^2

Then, the transformations that suffered were:

• Horizontal translation to the left 5 units


y=(x+5)^2

• Reflection over the x-axis


y=-(x+5)^2

• Vertical compression 2 units


y=-2(x+5)^2

• Vertical translation down 3 units


g(x)=-2(x+5)^(2)-3

User Rahul Katariya
by
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