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9.1 – Graphing Quadratic Functions. Ex. 1 Use a table of values to graph the following functions. a. y = 2 x 2 – 4 x – 5. Ex. 1 Use a table of values to graph the following functions. a. y = 2 x 2 – 4 x – 5. Ex. 1 Use a table of values to graph the following functions.
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Ex. 1 Use a table of values to graph the following functions. a. y = 2x2 – 4x – 5
Ex. 1 Use a table of values to graph the following functions. a. y = 2x2 – 4x – 5
Ex. 1 Use a table of values to graph the following functions. a. y = 2x2 – 4x – 5
Ex. 1 Use a table of values to graph the following functions. a. y = 2x2 – 4x – 5
Ex. 1 Use a table of values to graph the following functions. a. y = 2x2 – 4x – 5 y = 2(-2)2 – 4(-2) – 5
Ex. 1 Use a table of values to graph the following functions. a. y = 2x2 – 4x – 5 y = 2(-2)2 – 4(-2) – 5 y = 8 + 8 – 5 = 11
Ex. 1 Use a table of values to graph the following functions. a. y = 2x2 – 4x – 5 y = 2(-2)2 – 4(-2) – 5 y = 8 + 8 – 5 = 11
Ex. 1 Use a table of values to graph the following functions. a. y = 2x2 – 4x – 5 y = 2(-2)2 – 4(-2) – 5 y = 8 + 8 – 5 = 11
Ex. 1 Use a table of values to graph the following functions. a. y = 2x2 – 4x – 5
Ex. 1 Use a table of values to graph the following functions. a. y = 2x2 – 4x – 5
Ex. 1 Use a table of values to graph the following functions. a. y = 2x2 – 4x – 5
Axis of symmetry: x = - b 2a • Vertex:
Axis of symmetry: x = - b 2a • Vertex: (x, y)
Axis of symmetry: x = - b 2a • Vertex: (x, y), where the x = axis of sym.
Axis of symmetry: x = - b 2a • Vertex: (x, y), where the x = axis of sym. • Maximum vs. Minimum:
Axis of symmetry: x = - b 2a • Vertex: (x, y), where the x = axis of sym. • Maximum vs. Minimum: For ax2 + bx + c,
Axis of symmetry: x = - b 2a • Vertex: (x, y), where the x = axis of sym. • Maximum vs. Minimum: For ax2 + bx + c, • If a is positive, then the vertex is a Minimum.
Axis of symmetry: x = - b 2a • Vertex: (x, y), where the x = axis of sym. • Maximum vs. Minimum: For ax2 + bx + c, • If a is positive, then the vertex is a Minimum. • If a is negative, then the vertex is a Maximum.
Axis of symmetry: x = - b 2a • Vertex: (x, y), where the x-value = axis of sym. • Maximum vs. Minimum: For the form ax2 + bx + c, • If a is positive, then the vertex is a Minimum. • If a is negative, then the vertex is a Maximum. Ex. 2 Write the equation of the axis of symmetry, and find the coordinates of the vertex fo the graph of each function. Identify the vertex as a max or min. Then graph the function.
Axis of symmetry: x = - b 2a • Vertex: (x, y), where the x-value = axis of sym. • Maximum vs. Minimum: For the form ax2 + bx + c, • If a is positive, then the vertex is a Minimum. • If a is negative, then the vertex is a Maximum. Ex. 2 Write the equation of the axis of symmetry, and find the coordinates of the vertex fo the graph of each function. Identify the vertex as a max or min. Then graph the function. a. -x2 + 2x + 3
Axis of symmetry: x = - b 2a • Vertex: (x, y), where the x-value = axis of sym. • Maximum vs. Minimum: For the form ax2 + bx + c, • If a is positive, then the vertex is a Minimum. • If a is negative, then the vertex is a Maximum. Ex. 2 Write the equation of the axis of symmetry, and find the coordinates of the vertex fo the graph of each function. Identify the vertex as a max or min. Then graph the function. a. -x2 + 2x + 3 1) axis of sym.:
Axis of symmetry: x = - b 2a • Vertex: (x, y), where the x-value = axis of sym. • Maximum vs. Minimum: For the form ax2 + bx + c, • If a is positive, then the vertex is a Minimum. • If a is negative, then the vertex is a Maximum. Ex. 2 Write the equation of the axis of symmetry, and find the coordinates of the vertex fo the graph of each function. Identify the vertex as a max or min. Then graph the function. a. -x2 + 2x + 3 1) axis of sym.: x = - b 2a
Axis of symmetry: x = - b 2a • Vertex: (x, y), where the x-value = axis of sym. • Maximum vs. Minimum: For the form ax2 + bx + c, • If a is positive, then the vertex is a Minimum. • If a is negative, then the vertex is a Maximum. Ex. 2 Write the equation of the axis of symmetry, and find the coordinates of the vertex fo the graph of each function. Identify the vertex as a max or min. Then graph the function. a. -x2 + 2x + 3 1) axis of sym.: x = - b = - 2 2a 2(-1)
Axis of symmetry: x = - b 2a • Vertex: (x, y), where the x-value = axis of sym. • Maximum vs. Minimum: For the form ax2 + bx + c, • If a is positive, then the vertex is a Minimum. • If a is negative, then the vertex is a Maximum. Ex. 2 Write the equation of the axis of symmetry, and find the coordinates of the vertex fo the graph of each function. Identify the vertex as a max or min. Then graph the function. a. -x2 + 2x + 3 1) axis of sym.: x = - b = - 2 = -2 = 1 2a 2(-1) -2
Axis of symmetry: x = - b 2a • Vertex: (x, y), where the x-value = axis of sym. • Maximum vs. Minimum: For the form ax2 + bx + c, • If a is positive, then the vertex is a Minimum. • If a is negative, then the vertex is a Maximum. Ex. 2 Write the equation of the axis of symmetry, and find the coordinates of the vertex fo the graph of each function. Identify the vertex as a max or min. Then graph the function. a. -x2 + 2x + 3 1) axis of sym.: x = - b = - 2 = -2 = 1 2a 2(-1) -2 2) vertex:
Axis of symmetry: x = - b 2a • Vertex: (x, y), where the x-value = axis of sym. • Maximum vs. Minimum: For the form ax2 + bx + c, • If a is positive, then the vertex is a Minimum. • If a is negative, then the vertex is a Maximum. Ex. 2 Write the equation of the axis of symmetry, and find the coordinates of the vertex fo the graph of each function. Identify the vertex as a max or min. Then graph the function. a. -x2 + 2x + 3 1) axis of sym.: x = - b = - 2 = -2 = 1 2a 2(-1) -2 2) vertex: (x, y)
Axis of symmetry: x = - b 2a • Vertex: (x, y), where the x-value = axis of sym. • Maximum vs. Minimum: For the form ax2 + bx + c, • If a is positive, then the vertex is a Minimum. • If a is negative, then the vertex is a Maximum. Ex. 2 Write the equation of the axis of symmetry, and find the coordinates of the vertex fo the graph of each function. Identify the vertex as a max or min. Then graph the function. a. -x2 + 2x + 3 1) axis of sym.: x = - b = - 2 = -2 = 1 2a 2(-1) -2 2) vertex: (x, y) = (1,
Axis of symmetry: x = - b 2a • Vertex: (x, y), where the x-value = axis of sym. • Maximum vs. Minimum: For the form ax2 + bx + c, • If a is positive, then the vertex is a Minimum. • If a is negative, then the vertex is a Maximum. Ex. 2 Write the equation of the axis of symmetry, and find the coordinates of the vertex fo the graph of each function. Identify the vertex as a max or min. Then graph the function. a. -x2 + 2x + 3 1) axis of sym.: x = - b = - 2 = -2 = 1 2a 2(-1) -2 2) vertex: (x, y) = (1, ?)
Axis of symmetry: x = - b 2a • Vertex: (x, y), where the x-value = axis of sym. • Maximum vs. Minimum: For the form ax2 + bx + c, • If a is positive, then the vertex is a Minimum. • If a is negative, then the vertex is a Maximum. Ex. 2 Write the equation of the axis of symmetry, and find the coordinates of the vertex fo the graph of each function. Identify the vertex as a max or min. Then graph the function. a. -x2 + 2x + 3 1) axis of sym.: x = - b = - 2 = -2 = 1 2a 2(-1) -2 2) vertex: (x, y) = (1, ?) -x2 + 2x + 3
Axis of symmetry: x = - b 2a • Vertex: (x, y), where the x-value = axis of sym. • Maximum vs. Minimum: For the form ax2 + bx + c, • If a is positive, then the vertex is a Minimum. • If a is negative, then the vertex is a Maximum. Ex. 2 Write the equation of the axis of symmetry, and find the coordinates of the vertex fo the graph of each function. Identify the vertex as a max or min. Then graph the function. a. -x2 + 2x + 3 1) axis of sym.: x = - b = - 2 = -2 = 1 2a 2(-1) -2 2) vertex: (x, y) = (1, ?) -x2 + 2x + 3 -(1)2 + 2(1) + 3
Axis of symmetry: x = - b 2a • Vertex: (x, y), where the x-value = axis of sym. • Maximum vs. Minimum: For the form ax2 + bx + c, • If a is positive, then the vertex is a Minimum. • If a is negative, then the vertex is a Maximum. Ex. 2 Write the equation of the axis of symmetry, and find the coordinates of the vertex fo the graph of each function. Identify the vertex as a max or min. Then graph the function. a. -x2 + 2x + 3 1) axis of sym.: x = - b = - 2 = -2 = 1 2a 2(-1) -2 2) vertex: (x, y) = (1, ?) -x2 + 2x + 3 -(1)2 + 2(1) + 3 -1 + 2 + 3
Axis of symmetry: x = - b 2a • Vertex: (x, y), where the x-value = axis of sym. • Maximum vs. Minimum: For the form ax2 + bx + c, • If a is positive, then the vertex is a Minimum. • If a is negative, then the vertex is a Maximum. Ex. 2 Write the equation of the axis of symmetry, and find the coordinates of the vertex fo the graph of each function. Identify the vertex as a max or min. Then graph the function. a. -x2 + 2x + 3 1) axis of sym.: x = - b = - 2 = -2 = 1 2a 2(-1) -2 2) vertex: (x, y) = (1, ?) -x2 + 2x + 3 -(1)2 + 2(1) + 3 -1 + 2 + 3 = 4
Axis of symmetry: x = - b 2a • Vertex: (x, y), where the x-value = axis of sym. • Maximum vs. Minimum: For the form ax2 + bx + c, • If a is positive, then the vertex is a Minimum. • If a is negative, then the vertex is a Maximum. Ex. 2 Write the equation of the axis of symmetry, and find the coordinates of the vertex fo the graph of each function. Identify the vertex as a max or min. Then graph the function. a. -x2 + 2x + 3 1) axis of sym.: x = - b = - 2 = -2 = 1 2a 2(-1) -2 2) vertex: (x, y) = (1, ?) -x2 + 2x + 3 -(1)2 + 2(1) + 3 -1 + 2 + 3 = 4, so (1, 4)
Axis of symmetry: x = - b 2a • Vertex: (x, y), where the x-value = axis of sym. • Maximum vs. Minimum: For the form ax2 + bx + c, • If a is positive, then the vertex is a Minimum. • If a is negative, then the vertex is a Maximum. Ex. 2 Write the equation of the axis of symmetry, and find the coordinates of the vertex fo the graph of each function. Identify the vertex as a max or min. Then graph the function. a. -x2 + 2x + 3 1) axis of sym.: x = - b = - 2 = -2 = 1 2a 2(-1) -2 2) vertex: (x, y) = (1, ?) -x2 + 2x + 3 -(1)2 + 2(1) + 3 -1 + 2 + 3 = 4, so (1, 4) 3) Max OR Min.?
Axis of symmetry: x = - b 2a • Vertex: (x, y), where the x-value = axis of sym. • Maximum vs. Minimum: For the form ax2 + bx + c, • If a is positive, then the vertex is a Minimum. • If a is negative, then the vertex is a Maximum. Ex. 2 Write the equation of the axis of symmetry, and find the coordinates of the vertex fo the graph of each function. Identify the vertex as a max or min. Then graph the function. a. -x2 + 2x + 3 1) axis of sym.: x = - b = - 2 = -2 = 1 2a 2(-1) -2 2) vertex: (x, y) = (1, ?) -x2 + 2x + 3 -(1)2 + 2(1) + 3 -1 + 2 + 3 = 4, so (1, 4) 3) Max OR Min.? (1, 4) is a max b/c a is neg.
4) Graph: *Plot vertex:
4) Graph: *Plot vertex: (1, 4)
4) Graph: *Plot vertex: (1, 4) *Make a table based on vertex
4) Graph: *Plot vertex: (1, 4) * Make a table based on vertex