question graph the equation shown below by transforming the graph of the parent function. $y = -|x|$

Explanation:

Step1: Identify Parent Function

The parent function is ( y = |x| ), which is a V - shaped graph with vertex at the origin, opening upwards.

Step2: Analyze Transformation

The given function is ( y=-|x| ). The negative sign in front of the absolute - value function indicates a reflection over the x - axis. For a function ( y = f(x) ), the function ( y=-f(x) ) is the reflection of ( y = f(x) ) over the x - axis. So, we take the graph of ( y = |x| ) (which opens up) and reflect it over the x - axis, so it will open downwards, with the vertex still at the origin ((0,0)). To graph it, we can use some key points. For ( y = |x| ), when ( x = 0 ), ( y = 0 ); when ( x = 1 ), ( y = 1 ); when ( x=-1 ), ( y = 1 ). For ( y=-|x| ), when ( x = 0 ), ( y = 0 ); when ( x = 1 ), ( y=-1 ); when ( x=-1 ), ( y=-1 ). We can plot these points ((0,0)), ((1, - 1)), ((-1, - 1)), ((2,-2)), ((-2,-2)) etc. and draw the V - shaped graph opening downwards.

Answer:

The graph of ( y = -|x| ) is the reflection of the graph of ( y = |x| ) over the x - axis. It is a V - shaped graph with vertex at ((0,0)) opening downwards. Key points include ((0,0)), ((1, - 1)), ((-1, - 1)), ((2,-2)), ((-2,-2)) (and other points following the pattern ( y=-|x| )) which can be plotted to form the graph.