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Graphing Quadratic Equations in Standard Form

Graphing Quadratic Equations in Standard Form. y = ax 2 + bx + c. Graph y = x 2. Find Axis of Symmetry a = 1 b = 0 c = 0 To find the Vertex, Plug 0 back into y = x 2 for x. Vertex(0,0). x = 0. y = 0. y. x. Graph y = x 2. Min or Max?. Axis of Symmetry x = 0 Vertex (0,0)

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Graphing Quadratic Equations in Standard Form

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  1. Graphing Quadratic Equations in Standard Form y = ax2 + bx + c

  2. Graph y = x2 • Find Axis of Symmetry a = 1 b = 0 c = 0 To find the Vertex, Plug 0 back into y = x2for x. Vertex(0,0) x = 0 y = 0

  3. y x Graph y = x2 Min or Max? Axis of Symmetry x = 0 Vertex (0,0) Finish the table Reflect Points Across AoS. Connect with a smooth U-shape graph Roots? 1 at (0,0) y – intercept (0,0) Parent Function

  4. y x Graph y = -x2 Min or Max? Find Axis of Symmetry x = 0 Find Vertex (0,0) Finish the table Reflect Points Across AoS. Connect with a smooth U-shape graph y = x2 Roots? 1 at (0,0) y – intercept (0,0)

  5. y x Graph y = x2 - 4 a Find Axis of Symmetry x = 0 Find Vertex (0,-4) Finish the table Reflect Points Across AoS. Connect with a smooth U-shape graph y = x2

  6. y x Graph y = x2 - 6x + 5 x = 3 Find the Axis of Symmetry Find the Vertex Look at the Parent Function It’s next point is right 1, up 1 from the vertex The next point for y = x2 - 6x + 5 will also be right 1, up 1 from the vertex because they are related. The next point for y = x2 - 6x + 5 will be right 2, up 4 from the vertex just like the parent functions

  7. y x Graph y = - x2 + 6x - 5 x = 3 Does the graph open up or down? Down Find Axis of Symmetry x = 3 Find the Vertex (3,4) Is the Vertex a Max or Min? Max Find the y-intercept (0,-5) State the roots/solutions. (1,0) & (5,0)

  8. y x Graph y = 2x2 y = 2x2 Does the graph open up or down? up Find Axis of Symmetry x = 0 Find the Vertex (0,0) Is the Vertex a Max or Min? Min Find the y-intercept (0,0) State the roots/solutions. (0,0) Make a table

  9. y x Graph y = 2x2 + 4x + 5 Does the graph open up or down? up Find Axis of Symmetry x = -1 Find the Vertex (-1,3) Is the Vertex a Max or Min? Min Find the y-intercept (0,5) State the roots/solutions. none No need to make a table…we know how these work now.

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