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6.1 Graphing Quadratic Functions Parabola Axis of symmetry Vertex

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A Quadratic function Parts of the Quadratic function. CONSTANT TERM

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The graph of a Quadratic function is called a parabola. A Quadratic function

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Parabola are Symmetrical Axis of Symmetry, splits it down the middle

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Parabola are Symmetrical Points reflect across the axis of symmetry

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Parabola are Symmetrical The equation for the axis symmetry is

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The y – Intercept of a parabola If x = 0, then c is the y intercept

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The Vertex of the Parabola The Vertex is a point at the highest or lowest point of the graph of a parabola. The Vertex is on the axis of symmetry, so its x coordinate is found by

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Now that you have x of the Vertex how do you find the y x = 1

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How can you tell if the Vertex is the highest or lowest point. It all depends on “a”. If a > 0, the parabola If a<0, the parabola is opens upward.opens downward

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The Maximum or Minimum value is the y value of the vertex If the vertex is ( -3, 1), of f(x)= x 2 + 6x + 10, then the minimum value is 1. Since the parabola is opening upward it is the minimum.

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How to graph the parabola f(x) = 2- 4x + x 2 Rewrite the function. f(x) = x 2 -4x + 2 Find the y intercept: f(0) = 0 2 -4(0) + 2 = 2 (0, 2) Find the vertex: a = 1, b= -4

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How to graph the parabola f(x) = 2- 4x + x 2 Start a table using number higher and lower then 2, from the vertex. Plot points

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How to graph the parabola f(x) = 2- 4x + x 2 Connects the points.

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Graph the function. Show the y intercept, axis of symmetry and vertex f(x) = -x 2 + 2x + 3

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Graph the function. Show the y intercept, axis of symmetry and vertex f(x) = -x 2 + 2x + 3 Does the graph open up or down? What are a, b and c?

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Graph the function. Show the y intercept, axis of symmetry and vertex f(x) = -x 2 + 2x + 3 Does the graph open up or down?Down What are a, b and c? a = -1 b = 2 c = 3, so the y intercept is (0,3)

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Graph the function. Show the y intercept, axis of symmetry and vertex f(x) = -x 2 + 2x + 3 axis of symmetry is x = 1 What are a, b and c? a = -1The vertex is b = 2 c = 3

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Graph the function. Show the y intercept, axis of symmetry and vertex f(x) = -x 2 + 2x + 3 Plot the points

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Graph the function. Show the y intercept, axis of symmetry and vertex f(x) = -x 2 + 2x + 3 Connect the points

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Homework Page 291 # 15, 19, 23, 25, 33 – 43 odd

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Homework Page 291- 292 # 16, 22, 26, 32 - 42 even, 46, 47

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