Question

85 POINTS!!!!!! Describe the graph of y = -|x + 4| - 5. 9(For 85 points it should at least be a sentence or two)

Answer 1

Answer:

The graph is the shape of an inverted "V" and opens downwards.  

The vertex of the graph is (-4, -5) and its axis of symmetry is x = -4.  

When x > -4, every time x increases by 1 unit, y decreases by 1 unit.

When x < -4, every time x decreases by 1 unit, y decreases by 1 unit.

Step-by-step explanation:

Absolute value

• The bars either side of an expression or a value are the absolute value symbols.
• "Absolute value" means how far a value is from zero. Therefore, the absolute value of a number is its positive numerical value.
• An absolute value function is a function that contains an algebraic expression within absolute value symbols.

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General form of an absolute value function

$y=a|x-h|+k$

where:

• a controls the width of the "V".
• (h, k) is the vertex

• If a > 0 the graph opens upwards.
  If a < 0 the graph opens downwards.
• x = h is the axis of symmetry.
• If 0 < a < 1,  the graph is compressed.
  If a > 1 the graph is stretched.

Given absolute value function:

$y=-|x+4|-5$

Graph of the given absolute value function:

• As a < 0, the graph is the shape of an inverted "V" and opens downwards.  
• The vertex of the graph is (-4, -5).
• Its axis of symmetry is x = -4.  
• When x > -4, every time x increases by 1 unit, y decreases by 1 unit.
• When x < -4, every time x decreases by 1 unit, y decreases by 1 unit.