What polynomial function could be represented by the graph below
2 answers:
Answer: (B). F(x) = 2x² + 2x - 4
Step-by-step explanation:
Let us think about the parent function F(x) = x² to pick our answer.
Options A and C have only shifted 2 units down (showed by the "-2" at the end) and the function graphed is shifted four units down.
Between options B and D, one is shifted 2 units to the right, and one is shifted 2 units to the left. We need the one shifted 2 units to the left. This is shown by the "+2x" in option B meaning it is our answer.
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The dimensions of the image are twice the dimensions of the preimage,
which indicates that the transformation is a dilation.
- The transformation <em>T</em> is; <u>a dilation transformation with a scale factor of 2, D₂</u>
Reasons:
The transformation applied to ΔABC = T
The image of ΔABC following the transformation, T = ΔA'B'C'
The perimeter of ΔA'B'C' = Twice the perimeter of ΔABC
Therefore, we have;
A'B' + B'C' + A'C' = 2 × (AB + BC + AC)
Which gives
A'B' + B'C' + A'C' = 2·AB + 2·BC + 2·AC
By similar triangles, we have the ratio of corresponding sides as follows;
Which gives;
A'B' = 2·AB
Therefore;
- Triangle ΔA'B'C' is twice the dimension of triangle ΔABC, and <em>T</em> is <u>a dilation transformation with a scale factor of 2, D₂</u>
Learn more about dilation transformation here: