Notes-Graphing Quadratic Equations 3.1

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).

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?

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

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

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

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

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

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

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

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?

Notes-Graphing Quadratic Equations 3.1