Vertex Form of a Quadratic

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Vertex Form of a Quadratic : 

Vertex Form of a Quadratic Equation:

Slide 2: 

To review: Given K – shifts the graph k units up or down (positive – up, negative – down) H – shifts the graph h units up or down (positive – left, negative – right) A – if negative, reflects the graph over the x axis

Slide 3: 

Graph of a Quadratic: Vertex: (0, 0) Axis of Symmetry: x = 0 Vertex is a minimum point

Slide 4: 

The green graph is the graph of the function above while the purple graph Is the standard quadratic. Vertex: (-2, -3) Axis of Symmetry: x= -2 Vertex is a minimum

Slide 5: 

The red graph is the graph of the function above Vertex: (2, 4) Axis of symmetry: x = 2 Vertex is a maximium

Slide 6: 

As you can see from the previous graphs, you can find the vertex, axis of symmetry, and the maximum or minimum just by using the equation. Vertex: (h, k) (the opposite of “h” and “k”) Axis of symmetry: x = h (use the x coordinate of the vertex) If a is positive, the vertex is a minimum If a is negative, the vertex is a maximum

Slide 7: 

Find the vertex, the axis of symmetry, and determine the maximum or minimum. Vertex: (-5, -3) Axis of symmetry: x = -5 Vertex is a maximum Vertex: (4, -1) Axis of Symmetry: x = 4 Vertex is a minimum