9.1 – Graphing Quadratic Functions

Ex. 1 Use a table of values to graph the following functions. a. y = 2x 2 – 4x – 5

Ex. 1 Use a table of values to graph the following functions. a. y = 2x 2 – 4x – 5 xy

Ex. 1 Use a table of values to graph the following functions. a. y = 2x 2 – 4x – 5 xy

Ex. 1 Use a table of values to graph the following functions. a. y = 2x 2 – 4x – 5 xy

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

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 = – 5 = 11 xy

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 = – 5 = 11 xy

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 = – 5 = 11 xy

Ex. 1 Use a table of values to graph the following functions. a. y = 2x 2 – 4x – 5 xy

Ex. 1 Use a table of values to graph the following functions. a. y = 2x 2 – 4x – 5 xy

Ex. 1 Use a table of values to graph the following functions. a. y = 2x 2 – 4x – 5 xy

b. y = -x 2 + 4x – 1 xy

b. y = -x 2 + 4x – 1 xy

b. y = -x 2 + 4x – 1 xy

b. y = -x 2 + 4x – 1 xy

b. y = -x 2 + 4x – 1 xy

b. y = -x 2 + 4x – 1 xy

b. y = -x 2 + 4x – 1 xy

Axis of symmetry:

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 ax 2 + bx + c,

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.

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.

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.

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

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.:

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

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)

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

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:

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)

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,

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, ?)

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

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

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)

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) = 4

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) = 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 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) = 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 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) = 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 xy 14

4) Graph: *Plot vertex: (1, 4) * Make a table based on vertex xy 0 14

4) Graph: *Plot vertex: (1, 4) * Make a table based on vertex xy 0 14

4) Graph: *Plot vertex: (1, 4) * Make a table based on vertex xy

4) Graph: *Plot vertex: (1, 4) * Make a table based on vertex xy

4) Graph: *Plot vertex: (1, 4) * Make a table based on vertex xy

4) Graph: *Plot vertex: (1, 4) * Make a table based on vertex xy

4) Graph: *Plot vertex: (1, 4) * Make a table based on vertex xy

b. 2x 2 – 4x – 5

1) axis of sym.: 2) vertex: (x, y) = 3) Max OR Min.? 4) Graph:

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