Mrs. Rivas 𝒙 − 𝟓 𝒙 − 𝟔 𝒙 𝒙² −𝟓𝒙 𝒙 𝒙² −𝟔𝒙 − 𝟑 −𝟑𝒙 𝟏𝟓 − 𝟑 −𝟑𝒙 𝟏𝟖 Ida S. Baker H.S. b) 𝒙 𝟐 −𝟖𝒙+𝟏𝟓 a) − 𝒙 𝟐 +𝟗𝒙−𝟏𝟖 −( − + ) 𝒙² 𝟗𝒙 𝟏𝟖 𝟏𝟓×𝟏 𝟓×𝟑 −𝟏𝟓×−𝟏 −𝟓×−𝟑 𝟏𝟖×𝟏 𝟗×𝟐 𝟔×𝟑 −𝟏𝟖×−𝟏 −𝟗×−𝟐 −𝟔×−𝟑 𝒙 2 −𝟓𝒙−𝟑𝒙+𝟏𝟓 −(𝒙 2 −𝟔𝒙−𝟑𝒙+𝟏𝟖) 𝒙 − 𝟓 𝒙 − 𝟔 𝒙 𝒙² −𝟓𝒙 𝒙 𝒙² −𝟔𝒙 − 𝟑 −𝟑𝒙 𝟏𝟓 − 𝟑 −𝟑𝒙 𝟏𝟖 ( )( ) (𝒙−𝟓)(𝒙−𝟑) 𝒙−𝟓 𝒙−𝟑 −( )( ) −(𝒙−𝟔)(𝒙−𝟑) 𝒙−𝟔 𝒙−𝟑

International Studies Charter School. Mrs. Rivas International Studies Charter School. Section 4-1 Quadratic Function and Transformation Essential Question # 1: What is the vertex from of a quadratic function? 𝒚=𝒂 𝒙−𝒉 ²+𝒌 Answer:

International Studies Charter School. Mrs. Rivas International Studies Charter School. Section 4-1 Quadratic Function and Transformation

International Studies Charter School. Mrs. Rivas International Studies Charter School. Section 4-1 Quadratic Function and Transformation Graphing a Parabola 1. Identify and graph the vertex. (h, k) 2. Identify and draw the axis of symmetry. x = h 3. Find and plot one points on one side of the axis of symmetry. 4. Plot the corresponding on the other side of the axis of symmetry. 5. Sketch the graph.

International Studies Charter School. Mrs. Rivas International Studies Charter School. Section 4-1 Quadratic Function and Transformation Graph the function 𝒇 𝒙 = 𝟏 𝟐 𝒙 𝟐 . 𝒚=𝒂 𝒙−𝒉 ²+𝒌 Vertex (𝟎,𝟎) Axis-Symmetry. 𝒙=𝟎 𝒚= 𝟏 𝟐 (𝟐)² = 𝟏 𝟐 (𝟒) 𝒙=𝟐 =𝟐 (𝟐,𝟐) 𝒚= 𝟏 𝟐 (𝟒)² = 𝟏 𝟐 (𝟏𝟔) 𝒙=𝟒 =𝟖 (𝟒,𝟖)

International Studies Charter School. Mrs. Rivas International Studies Charter School. Section 4-1 Quadratic Function and Transformation 𝒚=𝒂 𝒙−𝒉 ²+𝒌 Vertex (𝟎,𝟎) Axis-Symmetry. 𝒙=𝟎 𝒚=− 𝟏 𝟑 (𝟑)² =− 𝟏 𝟑 (𝟗) 𝒙=𝟑 =−𝟑 (𝟑,−𝟑)

International Studies Charter School. Mrs. Rivas International Studies Charter School. Section 4-1 Quadratic Function and Transformation 𝒚=𝒂 𝒙−𝒉 ²+𝒌 Vertex (𝟎,−𝟓) Axis-Symmetry. 𝒙=𝟎 𝒙=𝟏 𝒚= 𝟏 2 −𝟓 =𝟏−𝟓 =−𝟒 (𝟏,−𝟒) 𝒙=𝟑 𝒚= 𝟑 2 −𝟓 =𝟗−𝟓 =𝟒 (𝟑,𝟒) Translation is 5 units down.

International Studies Charter School. Mrs. Rivas International Studies Charter School. Section 4-1 Quadratic Function and Transformation 𝒚=𝒂 𝒙−𝒉 ²+𝒌 Vertex (𝟒,𝟎) Axis-Symmetry. 𝒙=𝟒 𝒙=𝟓 𝒚= 𝟓−𝟒 2 =(𝟏)² =𝟏 (𝟓,𝟏) 𝒙=𝟔 𝒚= 𝟔−𝟒 2 =(𝟐)² =𝟒 (𝟔,𝟒) Translation is 4 units right.

International Studies Charter School. Mrs. Rivas International Studies Charter School. Section 4-1 Quadratic Function and Transformation 2. 𝒈 𝒙 =𝒙²+𝟑 3. 𝒉 𝒙 =(𝒙+𝟏)² Translation is 3 units up. Translation is 1 units left.

International Studies Charter School. Mrs. Rivas International Studies Charter School. Section 4-1 Quadratic Function and Transformation 4. 𝒇 𝒙 =𝟑 𝒙−𝟒 ²−𝟐 5. 𝒇 𝒙 =−𝟐 𝒙+𝟏 𝟐 +𝟒 Translation is 1 units left and 4 units up. Translation is 4 units right and 2 units down.

International Studies Charter School. Mrs. Rivas International Studies Charter School. Section 4-1 Quadratic Function and Transformation State weather the graph Reflects over the x-axis (𝒂 =− 𝟏), Stretch (𝒂 > 𝟏) or Shrinks (𝟎 < 𝒂 < 𝟏). A) 𝑦= 𝑥+2 2 +3 C) 𝑦=2 𝑥−1 2 +3 E) 𝑦= 1 2 𝑥+2 2 −1 Since 𝒂 = 𝟏 then the graph opens up. Since 𝒂> 𝟏 then the graph opens up and the graph stretches. Since 𝒂> 𝟏 then the graph opens up and the graph shrinks. F) 𝑦=− 1 3 𝑥+3 2 −5 B) 𝑦= − 𝑥+2 2 +3 D) 𝑦=−2 𝑥−1 2 +3 Since 𝒂> 𝟏 then the graph opens down and the graph stretches. Since 𝒂=−# then the graph opens down and the graph shrinks. Since 𝒂 = −𝟏 then the graph opens down and it reflects over the 𝒙.

International Studies Charter School. Mrs. Rivas International Studies Charter School. Section 4-1 Quadratic Function and Transformation Minimum and maximum value ** The minimum or maximum value is ALWAYS the 𝒚=𝒌.

International Studies Charter School. Mrs. Rivas International Studies Charter School. Section 4-1 Quadratic Function and Transformation What is the is the minimum or maximum value of the following graphs. A) B) Vertex (−𝟒,𝟐) Vertex (−𝟏,−𝟑) Since the graph opens up, it has a minimum value = -3. Since the graph opens down, it has a maximum value = 2.

International Studies Charter School. Mrs. Rivas International Studies Charter School. Section 4-1 Quadratic Function and Transformation Domain and Range [𝑲,∞) (−∞,𝒌] Vertex (𝒉,𝒌) ** The Domain (𝒉) is all the real numbers. (−∞,∞) ** The Range (𝒌) is all real numbers  (for minimum value) or  (for maximum value) than the value of 𝒌.

International Studies Charter School. Mrs. Rivas International Studies Charter School. Section 4-1 Quadratic Function and Transformation What is the is the domain and range of the following graphs. A) B) Vertex (−𝟒,𝟐) Vertex (−𝟏,−𝟑) Domain (h) = (-∞, ∞). Domain (h) = (-∞, ∞). Range (k) = [-3, ∞). Range (k) = (-∞, 2].

International Studies Charter School. Mrs. Rivas International Studies Charter School. Section 4-1 Quadratic Function and Transformation What is the vertex, axis of symmetry, the maximum or minimum, the domain and the range and the transformation of the parent function? 𝒂 =−𝟑 Vertex (𝟒,−𝟐) Axis-Symmetry. 𝒙=𝟒 Since a > 1 and negative the graph opens down and stretch. Since the graph opens down we have a maximum value of −𝟐. Domain (h) = all the real numbers. (-∞, ∞) Range (k) = all the real numbers ≤−𝟐. (-∞, -2] Transformation is 4 units right and 2 units down.

International Studies Charter School. Mrs. Rivas International Studies Charter School. Section 4-1 Quadratic Function and Transformation What is the vertex, axis of symmetry, the maximum or minimum, the domain and the range and the transformation of the parent function? 𝒂 =𝟎.𝟑 Vertex (−𝟏,𝟒) Axis-Symmetry. 𝒙=−𝟏 Since 0 < a < 1 and Positive the graph opens up and shrink. Since the graph opens up we have a minimum value of 𝟒. Domain (h) = all the real numbers. (-∞, ∞) Range (k) = all the real numbers ≥𝟒. [4,∞) Transformation is 1 units left and 4 units up.