Graphing Quadratic Equations a step-by-step guide with practice.

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Presentation transcript:

Graphing Quadratic Equations a step-by-step guide with practice

Graphing from Standard Form Graph y = x 2 – 6x + 8. go to next slide for step 1

Graphing from Standard Form Graph y = x 2 – 6x + 8. Step 1: Find the axis of symmetry. go to next slide for step 2

Graphing from Standard Form Graph y = x 2 – 6x + 8. Step 2: Find the vertex. Vertex: (3, – 1) go to next slide for step 3

Graphing from Standard Form Graph y = x 2 – 6x + 8. Step 3: Complete an x/y table. xy go to next slide for final graph

Graphing from Standard Form Graph y = x 2 – 6x + 8. What are the solutions? x = 2 and x = 4

Graphing from Standard Form Try this one: Graph y = – x 2 + 5x – 2.

Graphing from Standard Form Try this one: Graph y = – x 2 + 5x – 2.

Graphing from Intercept Form Graph y = (x – 4)(x + 2). go to next slide for step 1

Graphing from Intercept Form Graph y = (x – 4)(x + 2). Step 1: Find the x-intercepts. x – 4 = 0 x = 4 x + 2 = 0 x = – 2 go to next slide for step 2

Graphing from Intercept Form Graph y = (x – 4)(x + 2). Step 2: Find the axis of symmetry. go to next slide for step 3

Graphing from Intercept Form Graph y = (x – 4)(x + 2). Step 3: Complete an x/y table. xy go to next slide for final graph

Graphing from Intercept Form Graph y = (x – 4)(x + 2). What are the solutions? x = – 2 and x = 4

Graphing from Intercept Form Try this one: Graph y = (x + 3)(x + 1).

Graphing from Intercept Form Try this one: Graph y = (x + 3)(x + 1). What are the solutions? x = – 3 and x = – 1

Graphing from Vertex Form Graph y = 2(x – 1) go to next slide for step 1

Graphing from Vertex Form Graph y = 2(x – 1) Step 1: Find the vertex. vertex: (1, 3) go to next slide for step 2

Graphing from Vertex Form Graph y = 2(x – 1) Step 2: Find the axis of symmetry. go to next slide for step 3

Graphing from Vertex Form Graph y = 2(x – 1) Step 3: Complete an x/y table. xy go to next slide for final graph

Graphing from Vertex Form Graph y = 2(x – 1) What are the solutions? There are NO real solutions … later we will learn how to find the imaginary/complex solutions!

Graphing from Vertex Form Try this one: Graph y = – (x + 1) 2 + 2

Graphing from Vertex Form Try this one: Graph y = – (x + 1) 2 + 2