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Graphing Quadratic Equations: Vertex Form & Axis of Symmetry

Learn how to convert standard form equations to vertex form, find the vertex and axis of symmetry, and solve word problems using quadratic equations. Practice identifying values of a, b, and c to graph parabolas accurately.

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Graphing Quadratic Equations: Vertex Form & Axis of Symmetry

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  1. 1. Put the equation in standard form: 3. Find the axis of symmetry: (vertical line) Notes-Graphing Quadratic Equations 3.1 Steps to finding the vertex of a graph 2. Identify the values of a, b, and c. 4. Find your vertex (substitute your axis of symmetry back into the original equation and solve for y).

  2. If a is positive, then the parabola will open up. If a is negative, then the parabola will open down. Graph opens up or opens down?

  3. OPENS DOWN a = -1 b = 2 c = -1

  4. OPENS DOWN a = 1 b = -6 c = 5

  5. OPENS DOWN a = -2 b = -8 c = 1

  6. OPENS DOWN a = 1 b = 8 c = -2

  7. Converting to Vertex Form from Standard Form • Find the vertex point, (h, k): • a will be the a from the standard form equation. • 3. Substitute into y = a (x-h)2 + k

  8. Converting to Vertex Form from Standard Form • Convert y = 2x2 – 4x + 5 • Convert y = -x2 – 2x + 1 Vertex = (1, 3) Vertex form: y = 2(x-1)2 + 3 Vertex = (-1, 2) Vertex form: y = -(x+1)2 + 2

  9. Converting to Vertex Form from Standard Form • 3. y = 8x2 – 64x - 3 Vertex = (4, -131) Vertex form: y = 8(x-4)2 - 131

  10. Word Problem -revisited • Philip’s tossing of the rock can be represented by the equation: • h(t) = -16t2 + 48t + 64 • Using your knowledge of how to find the vertex from today’s lesson now answer the following questions. • Identify the vertex and the axis of symmetry of the graph. • b. What is the maximum height the rock reaches above the surface of the lake? • c. After how many seconds does the rock hit the surface of the lake?

  11. Class work Note-taking Guide Page 60-62 #5-13 and 24 Homework Page 60 – 61 #5-15, 37-39

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