Math  /  Algebra

Questionample 4: Write the equation y=2x83y=|-2 x-8|-3 in the form y=axp+qy=a|x-p|+q, then sketch the graph using transformations.  vertex =(p,q)=(4,3)\begin{aligned} \text { vertex } & =(p, q) \\ & =(-4,3) \end{aligned}

Studdy Solution
Sketch the graph using the transformations.
1. Start with the basic graph of y=x y = |x| .
2. Apply a vertical stretch by a factor of 2.
3. Shift the graph 4 units to the left.
4. Shift the graph 3 units downward.

The vertex of the graph is at (4,3) (-4, -3) , and the graph opens upwards with a slope of 2 on either side of the vertex.

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