Graphing Quadratic Equations

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Presentation transcript:

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

Graphing from Standard Form Graph y = x2 – 6x + 8.

Graphing from Standard Form Graph y = x2 – 6x + 8. Step 1: Find the axis of symmetry.

Graphing from Standard Form Graph y = x2 – 6x + 8. Step 2: Find the vertex. Vertex: (3, – 1)

Graphing from Standard Form Graph y = x2 – 6x + 8. Step 3: Graph using quadratic pattern.

Graphing from Standard Form Graph y = x2 – 6x + 8. What are the roots? (2,0) & (4,0)

Graphing from Intercept Form Graph y = (x – 4)(x + 2).

Graphing from Intercept Form Graph y = (x – 4)(x + 2). Step 1: Find the x-intercepts. x – 4 = 0 x = 4 (4,0) x + 2 = 0 x = – 2 (-2,0)

Graphing from Intercept Form Graph y = (x – 4)(x + 2). Step 2: Find the axis of symmetry.

Graphing from Intercept Form Graph y = (x – 4)(x + 2). Step 3: Graph using quadratic pattern.

Graphing from Intercept Form Graph y = (x – 4)(x + 2). What are the zeros? (– 2,0) & (4,0)

Graphing from Vertex Form Graph y = 2(x – 1)2 + 3

Graphing from Vertex Form Graph y = 2(x – 1)2 + 3 Step 1: Find the vertex. vertex: (1, 3)

Graphing from Vertex Form Graph y = 2(x – 1)2 + 3 Step 2: Find the axis of symmetry.

Graphing from Vertex Form Graph y = 2(x – 1)2 + 3 Step 3: Graph using quadratic pattern.

Graphing from Vertex Form Graph y = 2(x – 1)2 + 3 What are the solutions? There are NO real solutions because the graph doesn’t cross the x-axis….the solutions are actually imaginary/complex!