The function y = x² + 8x + 12 describes this graph. This is obtained by using equation of parabola at the origin and transforming the graph to the required position as in the question by using rules of transformation of linear function.
What are the Rules of Transformation of Linear Function?
Rules of transformation of linear function are
- f(x)+b - function is shifted b units upward
- f(x)-b - function is shifted b units downward
- f(x+b) - function is shifted b units to the left
- f(x-b) - function is shifted b units to the right
- -f(x) - function is reflected over x-axis
- f(-x) - function is reflected over y-axis
What is the required function?
Equation of parabola at the origin is y = x²
- First the graph is shifted left 4 units
By the transformation we can rewrite the function in f(x+b) form;
that is ⇒ y = (x+4)² ⇒ y = x² + 8x +16
- Next the graph is shifted 4 units downward
By the transformation we can rewrite the function in f(x)-b form;
that is ⇒ y = x² + 8x +16 - 4 ⇒ y = x² + 8x +12
This is the required function.
Hence the function y = x² + 8x + 12 describes this graph.
Learn more about transformation rules here:
brainly.com/question/17006186
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