Day 1­1.2 Forms of Quadratic Functions and Graph Vertex Form.notebook
September 08, 2016
Warm up: Solve: 1) |x + 7| = 2x ­ 1
2) 3|2x ­ 3| ­ 7 = 3x + 14
1.1 and 1.2 Quadratic Functions
Vertex Form
Standard Form
Intercept Form
Day 1­1.2 Forms of Quadratic Functions and Graph Vertex Form.notebook
September 08, 2016
I. Characteristics of Graph
1. Graph is u-shaped.
2. Opens up or down.
3. Has a vertex, the lowest or highest point on the graph.
lowest if opens up, highest if opens down.
4. Has an axis of symmetry, a vertical line through the
vertex that divides the parabola into two halves
that are mirror images.
5. Has a minimum or maximum value of the function, the
y-coordinate of the vertex.
2
II. Vertex Form y = a(x - h) + k
A. Identify characteristics
Example:
1. Direction of opening: up if a > 0; down if a < 0
2. Vertex (h, k) - (opposite, same)
3. Axis of symmetry - x-coordinate of vertex
4. Min. or max.?
Day 1­1.2 Forms of Quadratic Functions and Graph Vertex Form.notebook
September 08, 2016
Example: f(x) = -1/2 (x + 3)
2
Example: f(x) = -3x + 6
2
Example: y = -2 (x - 4) - 1
TRY: f(x) = (x + 5)
2
2
y = 5/2 (x + 3) - 2
2
Day 1­1.2 Forms of Quadratic Functions and Graph Vertex Form.notebook
September 08, 2016
B. Graph Vertex Form
f(x) = -1/2 (x + 3)
2
1.
2.
3.
4.
5.
6.
7.
8.
Identify direction opens.
Identify and plot vertex.
Set up x-y table; enter vertex.
Find next 2 x values by adding
denominator of "a" to previous
x value, twice.
Plug each new x value into the
function and find the
corresponding y value.
Plot the 2 new points.
Reflect both points across
the axis of symmetry.
Connect with smooth curve.
2
f(x) = -3x + 6
Domain:
Range:
Day 1­1.2 Forms of Quadratic Functions and Graph Vertex Form.notebook
September 08, 2016
2
y = -2 (x - 4) - 1
Domain:
Range:
2
y = 5/2 (x + 3) - 2
Domain:
Range: