Compare the graph of $n ( x ) = 7 ( x - 3 ) ^ { 2 } + 6$ with $n ( x ) = x ^ { 2 }$ .
A) $n ( x ) = 7 ( x - 3 ) ^ { 2 } + 6$ shifts left 3 units,shifts downward 6 units,and stretches by a factor of 7.
B) $n ( x ) = 7 ( x - 3 ) ^ { 2 } + 6$ shifts left 3 units,shifts upward 6 units,and stretches by a factor of 7.
C) $n ( x ) = 7 ( x - 3 ) ^ { 2 } + 6$ shifts right 3 units,shifts downward 6 units,and shrinks by a factor of $\frac { 1 } { 7 }$ .
D) $n ( x ) = 7 ( x - 3 ) ^ { 2 } + 6$ shifts right 3 units,shifts upward 6 units,and shrinks by a factor of $\frac { 1 } { 7 }$ .
E) $n ( x ) = 7 ( x - 3 ) ^ { 2 } + 6$ shifts right 3 units,shifts upward 6 units,and stretches by a factor of 7.

Question

Quizplus · Accepted Answer

The form $n(x) = 7(x - 3)^2 + 6$ indicates a transformation of the base graph $n(x) = x^2$. The term $(x - 3)$ indicates a horizontal shift to the right by 3 units (since it's in the form $x - h$, where $h$ is positive), the $+6$ indicates a vertical shift upward by 6 units, and the coefficient $7$ indicates a vertical stretch by a factor of 7, not a shrink.

Compare the Graph Of n(x)=7(x−3)2+6n ( x ) = 7 ( x - 3 ) ^ { 2 } + 6n(x)=7(x−3)2+6

Compare the Graph Of $n ( x ) = 7 ( x - 3 ) ^ { 2 } + 6$