Describe how the graph of the equation relates to the graph of y = x2.
-$$f ( x ) = - ( x + 7 ) ^ { 2 }$$
A) a translation 7 units to the left and a reflection across the x-axis
B) a translation 7 units to the right and a reflection across the y-axis
C) a translation 7 units to the right and a reflection across the x-axis
D) a translation 7 units up and a reflection across the x-axis

Question

Quizplus · Accepted Answer

The equation $f(x) = -(x + 7)^2$ represents a transformation of the graph of $y = x^2$. The negative sign outside the squared term indicates a reflection across the x-axis. The $+7$ inside the parentheses with $x$ indicates a translation 7 units to the left, not to the right, because the graph shifts in the opposite direction of the sign inside the parentheses.

Describe How the Graph of the Equation Relates to the Graph