Compare the graph of $p ( x ) = 4 ( x - 3 ) ^ { 2 } + 9$ with $p ( x ) = x ^ { 2 }$ .
A) $p ( x ) = 4 ( x - 3 ) ^ { 2 } + 9$ shifts right $3$ units, shifts downward $9$ units, and shrinks by a factor of $\frac { 1 } { 4 }$ .
B) $p ( x ) = 4 ( x - 3 ) ^ { 2 } + 9$ shifts right $3$ units, shifts upward $9$ units, and stretches by a factor of $4$ .
C) $p ( x ) = 4 ( x - 3 ) ^ { 2 } + 9$ shifts left $3$ units, shifts downward $9$ units, and stretches by a factor of $4$ .
D) $p ( x ) = 4 ( x - 3 ) ^ { 2 } + 9$ shifts right $3$ units, shifts upward $9$ units, and shrinks by a factor of $\frac { 1 } { 4 }$ .
E) $p ( x ) = 4 ( x - 3 ) ^ { 2 } + 9$ shifts left $3$ units, shifts upward $9$ units, and stretches by a factor of $4$ .

Question

Quizplus · Accepted Answer

The form $p(x) = a(x - h)^2 + k$ shows a parabola that has been shifted $h$ units to the right, $k$ units upward, and stretched or shrunk by a factor of $|a|$ when compared to $p(x) = x^2$. In this case, $h = 3$, $k = 9$, and $a = 4$, indicating a shift right by 3 units, an upward shift by 9 units, and a stretch by a factor of 4.

Compare the Graph Of p(x)=4(x−3)2+9p ( x ) = 4 ( x - 3 ) ^ { 2 } + 9p(x)=4(x−3)2+9

Compare the Graph Of $p ( x ) = 4 ( x - 3 ) ^ { 2 } + 9$