How to graph [tex]y = -4|x + 2| - 5[/tex]?

y = − 4∣ x + 2∣ − 5 x = − 6 ⇒ y = − 4∣ − 6 + 2∣ − 5 = − 4∣ − 4∣ − 5 = − 4 ∗ 4 − 5 = = − 16 − 5 = − 21 x = − 4 ⇒ y = − 4∣ − 4 + 2∣ − 5 = − 4∣ − 2∣ − 5 = − 4 ∗ 2 − 5 = = − 8 − 5 = − 13 x = − 2 ⇒ y = − 4∣ − 2 + 2∣ − 5 = − 4∣0∣ − 5 = − 4 ∗ 0 − 5 = − 5 x = 0 ⇒ y = − 4∣0 + 2∣ − 5 = − 4∣2∣ − 5 = − 4 ∗ 2 − 5 = − 8 − 5 = − 13 x = 2 ⇒ y = − 4∣2 + 2∣ − 5 = − 4∣4∣ − 5 = − 4 ∗ 4 − 5 = − 16 − 5 = − 21

Answered by Lilith | 2024-06-10

To graph y = − 4∣ x + 2∣ − 5 , identify key points by substituting values into the function, then plot these points to create the downward-opening V-shape. Ensure you account for the transformations, including a vertical stretch by 4 and a downward shift by 5. The vertex of the graph will be at ( − 2 , − 5 ) .
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Answered by Lilith | 2024-12-19