1. Honors Algebra 2 Chapter 4
Honors Algebra 2 Chapter Standard Form of a Quadratic Function f(x) = ax2 + bx + c

2. Graphing a Quadratic Function in Standard Form:
Step 1: Find the Axis of Symmetry
Step 2: Find the y-value of the vertex by substituting in the axis of Symmetry.
Step 3: Find the y-intercept: (0, C)
Step 4: Plot the axis of symmetry, vertex and y-intercept
Step 5: Reflect the y-intercept about the axis of symmetry for a third point

3. Example : Graph the quadratic function f(x) = 4x2 – 12x + 9
1. Axis of symmetry:
2. Vertex: y = 4(1.5)2 – 12(1.5) + 9 = 0 Vertex (1.5, 0)
3. Y-intercept (0, 9)
4. Plot:
5. Reflect the y-intercept about the axis of symmetry for a third point.

4. Converting Standard Form to Vertex Form
y = ax2 + bx + c to
y = a(x – h) + k
Step 1: Identify “a”
Step 2: Find the axis of symmetry
Step 3: Determine the y-value of the vertex
Step 4: Plug in “a”, “h” and “k”
Example: Write the quadratic function f(x) = 2x2 – 5x in vertex form.
1. “a” = 2
2. Axis of symmetry:
3. Vertex: x = 1.25
y = 2(1.25)2 – 5(1.25) + 12 = 8.875
Vertex (1.25, 8.875)
4. Plug in values: y = 2(x – 1.25)

5. Standard Form of a Quadratic Function
Honors Algebra 2
Chapter 4.2
Standard Form of a Quadratic Function
Homework
Pages #9, 10, 19, 26, 27, 28, 32, 33, 34, 35, 43, 45, 49, 50, 52