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Graphing Quadratic Functions - Axis of Symmetry and Vertex

Learn how to find the axis of symmetry and vertex of a parabola to effectively graph quadratic functions. Practice graphing three parabolas in class and complete the assigned worksheet for homework.

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Graphing Quadratic Functions - Axis of Symmetry and Vertex

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  1. Warm Up Find five points and use them to graph Hint, use an x-y table to help you 

  2. 11-1 Graphing Quadratic Functions Objective: To find and use the axis of symmetry and the vertex of a parabola to graph it. Standard 21.0

  3. Graph for Warm Up This “U” shape is called a parabola. Magic Ordered Pairs (1,1a) (2,4a) (3,9a) Use these every time When A,B,C change, moves vertex but does not change the shape Vertex Turning point (0,0) On axis of symmetry Axis of Symmetry Cuts parabola in half Reflects over line x = 0 Quadratic Function: y = Ax2 + Bx + C A,B,C are integers

  4. Looks like.. A parabola can also make shape. To tell which way it points, look at the a value a (+) = + + minimum (vertex) A (-) = – – maximum (vertex)

  5. Examples Standard Form Opens Up or Down Find the axis of symmetry Find the vertex Graph using the parent function a(+) = up/min a(-) = down/max Plug in x to standard form y = ax2 + bx + c x = – b 2a (1,1) (2,4) (3,9) reflect y = 1x2 + 0x + 0 a = 1 b = 0 c = 0 y = x2 x = 0 2(1) Up Vertex Minimum x = 0 y = (0)2 y = 0 (0,0) This is the same graph as the warm up!

  6. “11-1 Graphing Quadratic Functions” Worksheet Follow along and fill in the worksheet with me. We will graph 3 parabolas today in class You will complete tonight’s homework on a similar worksheet so… Take good notes in class so you can use them to help you do the homework! 

  7. HOMEWORK • Page 615 #Pg. 615 # 15, 16, 19, 25, 28 • To be done on worksheet given in class • Answers include: Up/down? Min/Max? Axis of Symmetry Vertex Graph 15) y = 4x2 1 6)y = -x2 + 4x – 1 19) y = x2 – 5 25) y = -3x2 – 6x + 4 28) y = -(x-2)2 + 1

  8. Extra Practice! The following 2 parabolas can be graphed and studied for extra practice 

  9. Examples Standard Form Opens Up or Down Find the axis of symmetry Find the vertex Graph using the parent function a(+) = up a(-) = down Plug in x to standard form (1,1) (2,4) (3,9) reflect ax2 + bx + c = y x = – b 2a y = x2 – 2x – 3 Up Vertex Minimum y = x2 – 2x – 3 a = 1 b = -2 c = -3 x = -(-2) 2(1) x = 1 y = (1)2 – 2(1) – 3 y = 1 – 2 – 3 y = -4 (1,-4)

  10. Examples Standard Form Opens Up or Down Find the axis of symmetry Find the vertex Graph using the parent function a(+) = up a(-) = down Plug in x to standard form (1,1) (2,4) (3,9) reflect ax2 + bx + c = y x = – b 2a y = x2 + 4x + 4 Up Vertex Minimum y = x2 + 4x + 4 a = 1 b = 4 c = 4 x = -(4) 2(1) x = -2 y = (-2)2 + 4(-2) + 4 y = 4 – 8 +4 y = 0 (-2,0)

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