S1 3rd Pd.notebook
November 12, 2015
Graph Quadratic Functions in Vertex Form
Graph .
What's the name of the shape?
How can we describe it?
What vocabulary do we associate with it?
S1 3rd Pd.notebook
November 12, 2015
S1 3rd Pd.notebook
Graph y = 2(x ­ 1)2 + 3
Step 1 ­ Identify the values for a, h, and k.
a =
h = k =
What is the vertex of the parabola?
Will the parabola open up or down?
Step 2 ­ Plot the vertex and axis of symmetry.
Step 3 ­ Find at least two other points to graph.
You should include at least one point to the
left of the vertex and one to the right ­
you can use the number line to help!
Step 4 ­ Connect the points and draw the parabola.
November 12, 2015
S1 3rd Pd.notebook
November 12, 2015
S1 3rd Pd.notebook
November 12, 2015
So vertex form uses transformations, like we talked about in Chapter 2. . .
The vertex form of a quadratic function is really about using translations to move the vertex of a parabola.
The variable h shows how far the graph is shifted sideways, and the variable k shows the vertical shift.
So the new vertex is the point (h, k) and the axis of symmetry has equation x = h.
The variable a describes the direction and width of the parabola.
You might even remember that we saw the variables h, k, and a when we graphed absolute value functions in Chapter 2.
S1 3rd Pd.notebook
November 12, 2015
Now graph these:
1)
y = ­(x + 2)2 ­ 3
2)
y = 1/2(x ­ 3)2 + 2
3)
2
y = 3x ­ 1
S1 3rd Pd.notebook
November 12, 2015
S1 3rd Pd.notebook
November 12, 2015
S1 3rd Pd.notebook
November 12, 2015
S1 3rd Pd.notebook
November 12, 2015