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?
2
Graph y = 2(x - 1) + 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.
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.
Now graph these:
1)
2)
3)
2
y = -(x + 2) - 3
2
y = 1/2(x - 3) + 2
2
y = 3x - 1
Let's practice graphing using the calculator -
Now let's do this backwards can we write some quadratic functions?
Use vertex form to write the equation of the parabola with vertex (3, -2)
that passes through the point (2, 3).
Write equations for these parabolas:
A. vertex (1/2, 1) and point (2, -8)
B. vertex (-12.5, 35.5) and point (1, 400)