Questions: Graphs and Functions Graphing an absolute value equation in the plane: Advanced Graph the equation. y=-4x+4+3

Transcript text: Graphs and Functions Graphing an absolute value equation in the plane: Advanced Graph the equation. \[ y=-4|x+4|+3 \]

Solution

Solution Steps

Step 1: Find the vertex.

The vertex of the absolute value function _y_ = _a_|_x_ - _h_| + _k_ is at the point (_h_, _k_). In this case, the function is _y_ = -4|_x_ + 4| + 3, so _h_ = -4 and _k_ = 3. The vertex is at (-4, 3).

Step 2: Determine the slope.

The slope of the branches of the absolute value function is given by _a_. In this case, _a_ = -4. Since _a_ is negative, the graph opens downward.

Step 3: Plot points.

Starting from the vertex (-4, 3), move one unit to the right and four units down (slope = -4). This gives the point (-3,-1). From the vertex, move one unit to the left and four units down. This gives the point (-5, -1).

Step 4: Draw the graph.

Draw lines connecting the vertex to the points (-3, -1) and (-5, -1) and extending outwards. These lines form the graph of the absolute value function.