Graphing 𝑓 𝑥 = 𝑎𝑥 2 +𝑐 Notes 8.2

 Example 1: Graphing 𝑦= 𝑥 2 +𝑐 Graph 𝑓(𝑥)= 𝑥 2 and 𝑔 𝑥 = 𝑥 2 −2. Compare g(x) to the graph of the parent function.

You Try! Graph the function. Compare the graph to the graph of 𝑓(𝑥)= 𝑥 2 . 1. 𝑓 𝑥 = 𝑥 2 −5 2. 𝑓 𝑥 = 𝑥 2 +3

Example 2: Graphing 𝑦= 𝑎𝑥 2 +𝑐 Graph 𝑓(𝑥)= 𝑥 2 and ℎ 𝑥 = 4𝑥 2 +1. Compare h(x) to the graph of the parent function.

You Try! Graph the function. Compare the graph to the graph of 𝑓(𝑥)= 𝑥 2 . 3. 𝑓 𝑥 = 2𝑥 2 −5 4. 𝑓 𝑥 = − 1 4 𝑥 2 +4

Example 4: Solving a Real-Life Problem   The function 𝑓 𝑥 = −16𝑡 2 + 𝑠 0 represents the approximate height (in feet) of a falling object t seconds after it is dropped from an initial height 𝑠 0 (in feet). An egg is dropped from a height of 64 feet. After how many seconds does the egg hit the ground?

You Try! 7. WHAT IF? The egg is dropped from a height of 100 feet. After how many seconds does the egg hit the ground?