MPM2D Graphing Parabolas of y ax h2 k form
When graphing parabolas, you only need two pieces of information. 1. The Vertex 2. The Direction of Opening and the Step Pattern.
From Day 1 of graphing parabolas: - We investigated the form y x 2 k
The Vertex was:
The Axis of Symmetry was:
The Direction of Opening was:
The Step Pattern was:
Therefore, the k-value represents the y-coordinate of the vertex.
From Day 2 of graphing parabolas: - We investigated the form y x h2
The Vertex was:
The Axis of Symmetry was:
The Direction of Opening was:
The Step Pattern was:
Therefore, the h-value represents the x-coordinate of the vertex.
From Day 3 of graphing parabolas: - We investigated the form y ax 2
The Vertex was:
The Axis of Symmetry was:
The Direction of Opening was:
The Step Pattern was:
Therefore, the a-value represents the step pattern and direction of opening. If we are given the equation of a parabola in y ax h2 k form, the vertex will be the point (h, k) and the step pattern will be a(1, 3, 5). If a is positive, the parabola will open up, if a is negative, the parabola will open down. Using this information, we can graph any parabola.
We must, however, learn to describe the transformations of the graph y x 2 based on the a, h and k values.
Ex.1. Describe the transformations on the graph y x 2 to get the following graphs: a. y 2x 2 4 b. y x 32
1 c. y 2x 42 6 d. y x 62 3 2
Ex.2. Sketch each of the above graphs on the grid to the right based on the vertex, direction of opening and the step pattern. Then state the domain and range of each function. Ex. Write an equation for the parabola with the given vertex and passing through the given point.
a. vertex (-2, 7), point (3, 5)
b. vertex (1, 2), y-intercept of (0, 4)
Homework – Pg. 223. Q 1-8,10,20,21