ALGEBRA II
5.1: GRAPHING QUADRATIC FUNCTIONS
Quadratic Function: f(x) = ax2 + bx + c, where a ¹ 0
Axis of Symmetry:
Vertex:
EX. 1: Graph f(x) = 2x2 – 8x + 9 by making a table of values. Give the axis of symmetry and vertex.
EX. 1b: Graph f(x) = x2 + 3x – 1 by making a table of values. Give the axis of symmetry and vertex.
Rules to Graph Quadratic Equations:
1. Find the y-intercept: Let x = 0 and solve for y
2. Find the axis of symmetry: Equation is
3. Find the vertex: x-coordinate is , plug into your equation to get the y-coordinate.
EX. 2: Consider the quadratic function f(x) = x2 + 9 + 8x.
a. Find the y-intercept, the equation of the axis of symmetry, and the vertex.
b. Make a table of values that includes the vertex
c. Graph the function.
EX. 2b: Consider the quadratic function f(x) = 2 – 4x + x2.
a. Find the y-intercept, the equation of the axis of symmetry, and the vertex.
b. Make a table of values that includes the vertex
c. Graph the function.
Maximum and Minimum Values of f(x) = ax2 + bx + c
1. The graph opens up and has a minimum when a is positive.
2. The graph opens down and has a maximum when a is negative.
· The min. or max. is the y value of the vertex.
EX. 3: Consider the function f(x) = x2 – 4x + 9.
a. Determine whether the function has a maximum or minimum value
b. State the maximum or minimum value of the function.
c. State the domain and range of the function.
EX. 3b: Consider the function f(x) = -x2 + 2x + 3.
a. Determine whether the function has a maximum or minimum value
b. State the maximum or minimum value of the function.
c. State the domain and range of the function.