Compare the graph of $s ( x ) = 5 ( x - 5 ) ^ { 2 } + 9$ with $s ( x ) = x ^ { 2 }$.
$s ( x ) = 5 ( x - 5 ) ^ { 2 } + 9$ shifts right 5 units, shifts downward 9 units, and shrinks by a
A) factor of $\frac { 1 } { 5 }$.
B) $s ( x ) = 5 ( x - 5 ) ^ { 2 } + 9$ shifts right 5 units, shifts upward 9 units, and stretches by a factor of 5 .
C) $s ( x ) = 5 ( x - 5 ) ^ { 2 } + 9$ shifts left 5 units, shifts downward 9 units, and stretches by a factor of 5 .
D) $s ( x ) = 5 ( x - 5 ) ^ { 2 } + 9$ shifts right 5 units, shifts upward 9 units, and shrinks by a factor of $\frac { 1 } { 5 }$.
E) $s ( x ) = 5 ( x - 5 ) ^ { 2 } + 9$ shifts left 5 units, shifts upward 9 units, and stretches by a factor of 5 .

Question

Quizplus · Accepted Answer

The equation $s(x) = 5(x - 5)^2 + 9$ represents a transformation of the base function $s(x) = x^2$. The term $(x - 5)^2$ indicates a horizontal shift to the right by 5 units (since we are moving in the positive direction to maintain the inside of the parenthesis as zero). The multiplication by 5 outside the squared term indicates a vertical stretch by a factor of 5, making the graph steeper. Lastly, the addition of 9 at the end of the equation represents a vertical shift upwards by 9 units.

Compare the Graph Of s(x)=5(x−5)2+9s ( x ) = 5 ( x - 5 ) ^ { 2 } + 9s(x)=5(x−5)2+9

Compare the Graph Of $s ( x ) = 5 ( x - 5 ) ^ { 2 } + 9$