Unit 1 : Graphing in Vertex Form
By: Mrinal Bhavsar
Learning Goal
My learning goal for the unit of graphing with vertex form is to be able to identify key information provided in the question or equation.
Summary of the Unit
When a quadratic relation is graphed it creates a symmetrical curve which is also known as a parabola. The points of the vertex are the coordinates at which the parabola start. On the vertex is also located the axis of symmetry which is used to display both equal sides of the graph. The vertex form equation of the parabola is required in order to define the transformations that may be made to the parabola. The equation y = a (x - h)² + k is used to make the transformations on y = x².
The a value in this equation defines the width and direction of opening of the parabola. This means that if:
- the value of a is greater than 1, then the parabola will be vertically stretched.
- the value of a is less than 1, then the parabola will be vertically condensed.
- the value of a is positive, then the parabola will open upwards.
- the value of a is negative, then the parabola will open downwards.
Graph
Here is an example of a parabola graphed in vertex form. In this graph the value of a is 1, so there is no change in the width or direction of opening. The value of h is -1 (inside the brackets), therefore the vertex is horizontally shifted 1 point to the right on the x-axis. The value of k in this graph is 1, therefore the vertex is vertically shifted 1 point up on the y-axis.
Solving Word Problems Using Vertex Form
The height of a ball, h meters, t seconds after it is thrown is given by the equation
h = -5 (t - 3)² + 46.5
a) what was the maximum height?
b) how long does it take the ball to reach its maximum height?
c) what was the height of the ball when it was thrown?
d)what was the height of the ball after 1 second?
(please click on image to view answers and work)
Video of Graphing Using Transformations
Website Assignment Part 4