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9.1 – Graphing Quadratic Functions
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Ex. 1 Use a table of values to graph the following functions. a. y = 2x 2 – 4x – 5
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Ex. 1 Use a table of values to graph the following functions. a. y = 2x 2 – 4x – 5 xy
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Ex. 1 Use a table of values to graph the following functions. a. y = 2x 2 – 4x – 5 xy -2 0 1 2
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Ex. 1 Use a table of values to graph the following functions. a. y = 2x 2 – 4x – 5 xy -2 0 1 2
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Ex. 1 Use a table of values to graph the following functions. a. y = 2x 2 – 4x – 5 y = 2(-2) 2 – 4(-2) – 5 xy -2 0 1 2
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Ex. 1 Use a table of values to graph the following functions. a. y = 2x 2 – 4x – 5 y = 2(-2) 2 – 4(-2) – 5 y = 8 + 8 – 5 = 11 xy -2 0 1 2
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Ex. 1 Use a table of values to graph the following functions. a. y = 2x 2 – 4x – 5 y = 2(-2) 2 – 4(-2) – 5 y = 8 + 8 – 5 = 11 xy -211 0 1 2
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Ex. 1 Use a table of values to graph the following functions. a. y = 2x 2 – 4x – 5 y = 2(-2) 2 – 4(-2) – 5 y = 8 + 8 – 5 = 11 xy -211 1 0-5 1-7 2-5
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Ex. 1 Use a table of values to graph the following functions. a. y = 2x 2 – 4x – 5 xy -211 1 0-5 1-7 2-5
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Ex. 1 Use a table of values to graph the following functions. a. y = 2x 2 – 4x – 5 xy -211 1 0-5 1-7 2-5
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Ex. 1 Use a table of values to graph the following functions. a. y = 2x 2 – 4x – 5 xy -211 1 0-5 1-7 2-5
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b. y = -x 2 + 4x – 1 xy -2 0 1 2
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b. y = -x 2 + 4x – 1 xy -2-13 -6 0 12 23
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b. y = -x 2 + 4x – 1 xy -2-13 -6 0 12 23
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b. y = -x 2 + 4x – 1 xy -2-13 -6 0 12 23 3 4
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b. y = -x 2 + 4x – 1 xy -2-13 -6 0 12 23 32 4
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b. y = -x 2 + 4x – 1 xy -2-13 -6 0 12 23 32 4
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b. y = -x 2 + 4x – 1 xy -2-13 -6 0 12 23 32 4
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Axis of symmetry:
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Axis of symmetry: x = - b 2a
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Vertex:
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Axis of symmetry: x = - b 2a Vertex: (x, y)
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Axis of symmetry: x = - b 2a Vertex: (x, y), where the x = axis of sym.
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Axis of symmetry: x = - b 2a Vertex: (x, y), where the x = axis of sym. Maximum vs. Minimum:
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Axis of symmetry: x = - b 2a Vertex: (x, y), where the x = axis of sym. Maximum vs. Minimum: For ax 2 + bx + c,
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Axis of symmetry: x = - b 2a Vertex: (x, y), where the x = axis of sym. Maximum vs. Minimum: For ax 2 + bx + c, –If a is positive, then the vertex is a Minimum.
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Axis of symmetry: x = - b 2a Vertex: (x, y), where the x = axis of sym. Maximum vs. Minimum: For ax 2 + bx + c, –If a is positive, then the vertex is a Minimum. –If a is negative, then the vertex is a Maximum.
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Axis of symmetry: x = - b 2a Vertex: (x, y), where the x-value = axis of sym. Maximum vs. Minimum: For the form ax 2 + 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.
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Axis of symmetry: x = - b 2a Vertex: (x, y), where the x-value = axis of sym. Maximum vs. Minimum: For the form ax 2 + 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. -x 2 + 2x + 3
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Axis of symmetry: x = - b 2a Vertex: (x, y), where the x-value = axis of sym. Maximum vs. Minimum: For the form ax 2 + 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. -x 2 + 2x + 3 1) axis of sym.:
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Axis of symmetry: x = - b 2a Vertex: (x, y), where the x-value = axis of sym. Maximum vs. Minimum: For the form ax 2 + 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. -x 2 + 2x + 3 1) axis of sym.: x = - b 2a
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Axis of symmetry: x = - b 2a Vertex: (x, y), where the x-value = axis of sym. Maximum vs. Minimum: For the form ax 2 + 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. -x 2 + 2x + 3 1) axis of sym.: x = - b = - 2 2a 2(-1)
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Axis of symmetry: x = - b 2a Vertex: (x, y), where the x-value = axis of sym. Maximum vs. Minimum: For the form ax 2 + 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. -x 2 + 2x + 3 1) axis of sym.: x = - b = - 2= -2 = 1 2a 2(-1) -2
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Axis of symmetry: x = - b 2a Vertex: (x, y), where the x-value = axis of sym. Maximum vs. Minimum: For the form ax 2 + 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. -x 2 + 2x + 3 1) axis of sym.: x = - b = - 2= -2 = 1 2a 2(-1) -2 2) vertex:
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Axis of symmetry: x = - b 2a Vertex: (x, y), where the x-value = axis of sym. Maximum vs. Minimum: For the form ax 2 + 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. -x 2 + 2x + 3 1) axis of sym.: x = - b = - 2= -2 = 1 2a 2(-1) -2 2) vertex: (x, y)
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Axis of symmetry: x = - b 2a Vertex: (x, y), where the x-value = axis of sym. Maximum vs. Minimum: For the form ax 2 + 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. -x 2 + 2x + 3 1) axis of sym.: x = - b = - 2= -2 = 1 2a 2(-1) -2 2) vertex: (x, y) = (1,
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Axis of symmetry: x = - b 2a Vertex: (x, y), where the x-value = axis of sym. Maximum vs. Minimum: For the form ax 2 + 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. -x 2 + 2x + 3 1) axis of sym.: x = - b = - 2= -2 = 1 2a 2(-1) -2 2) vertex: (x, y) = (1, ?)
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Axis of symmetry: x = - b 2a Vertex: (x, y), where the x-value = axis of sym. Maximum vs. Minimum: For the form ax 2 + 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. -x 2 + 2x + 3 1) axis of sym.: x = - b = - 2= -2 = 1 2a 2(-1) -2 2) vertex: (x, y) = (1, ?) -x 2 + 2x + 3
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Axis of symmetry: x = - b 2a Vertex: (x, y), where the x-value = axis of sym. Maximum vs. Minimum: For the form ax 2 + 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. -x 2 + 2x + 3 1) axis of sym.: x = - b = - 2= -2 = 1 2a 2(-1) -2 2) vertex: (x, y) = (1, ?) -x 2 + 2x + 3 -(1) 2 + 2(1) + 3
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Axis of symmetry: x = - b 2a Vertex: (x, y), where the x-value = axis of sym. Maximum vs. Minimum: For the form ax 2 + 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. -x 2 + 2x + 3 1) axis of sym.: x = - b = - 2= -2 = 1 2a 2(-1) -2 2) vertex: (x, y) = (1, ?) -x 2 + 2x + 3 -(1) 2 + 2(1) + 3 -1 + 2 + 3
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Axis of symmetry: x = - b 2a Vertex: (x, y), where the x-value = axis of sym. Maximum vs. Minimum: For the form ax 2 + 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. -x 2 + 2x + 3 1) axis of sym.: x = - b = - 2= -2 = 1 2a 2(-1) -2 2) vertex: (x, y) = (1, ?) -x 2 + 2x + 3 -(1) 2 + 2(1) + 3 -1 + 2 + 3 = 4
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Axis of symmetry: x = - b 2a Vertex: (x, y), where the x-value = axis of sym. Maximum vs. Minimum: For the form ax 2 + 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. -x 2 + 2x + 3 1) axis of sym.: x = - b = - 2= -2 = 1 2a 2(-1) -2 2) vertex: (x, y) = (1, ?) -x 2 + 2x + 3 -(1) 2 + 2(1) + 3 -1 + 2 + 3 = 4, so (1, 4)
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Axis of symmetry: x = - b 2a Vertex: (x, y), where the x-value = axis of sym. Maximum vs. Minimum: For the form ax 2 + 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. -x 2 + 2x + 3 1) axis of sym.: x = - b = - 2= -2 = 1 2a 2(-1) -2 2) vertex: (x, y) = (1, ?) -x 2 + 2x + 3 -(1) 2 + 2(1) + 3 -1 + 2 + 3 = 4, so (1, 4) 3) Max OR Min.?
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Axis of symmetry: x = - b 2a Vertex: (x, y), where the x-value = axis of sym. Maximum vs. Minimum: For the form ax 2 + 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. -x 2 + 2x + 3 1) axis of sym.: x = - b = - 2= -2 = 1 2a 2(-1) -2 2) vertex: (x, y) = (1, ?) -x 2 + 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.
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4) Graph:
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*Plot vertex:
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4) Graph: *Plot vertex: (1, 4)
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4) Graph: *Plot vertex: (1, 4) *Make a table based on vertex
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4) Graph: *Plot vertex: (1, 4) * Make a table based on vertex xy 14
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4) Graph: *Plot vertex: (1, 4) * Make a table based on vertex xy 0 14
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4) Graph: *Plot vertex: (1, 4) * Make a table based on vertex xy 0 14
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4) Graph: *Plot vertex: (1, 4) * Make a table based on vertex xy 0 14 2
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4) Graph: *Plot vertex: (1, 4) * Make a table based on vertex xy 0 14 2 3
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4) Graph: *Plot vertex: (1, 4) * Make a table based on vertex xy 0 03 14 23 30
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4) Graph: *Plot vertex: (1, 4) * Make a table based on vertex xy 0 03 14 23 30
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4) Graph: *Plot vertex: (1, 4) * Make a table based on vertex xy 0 03 14 23 30
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b. 2x 2 – 4x – 5
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1) axis of sym.: 2) vertex: (x, y) = 3) Max OR Min.? 4) Graph:
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b. 2x 2 – 4x – 5 1) axis of sym.: x = - b = -(-4)= 4 = 1 2a 2(2) 4 2) vertex: (x, y) = (1, ?) 2x 2 – 4x – 5 2(1) 2 – 4(1) – 5 2 – 4 – 5 = -7, so (1, -7) 3) Max OR Min.? (1, -7) is a min b/c a is neg. 4) Graph: *Plot vertex: (1, -7) * Make a table based on vertex xy 1 0-5 1-7 2-5 31
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