Prepared By: Dwight Williams
Graphing Vertex Form
Learning Checkpoint of Unit
- I can use the mapping formula to graph vertex form equations
- I can solve word problems using the vertex form
Using Finite Differences To Find a Quadratic Function
Quadratic functions/parabolas can be written in the form: y = a(x – h)2 + k
In a quadratic function/parabola there is a Vertex, the Optimal Value, and the Axis of Symmetry(AOS)
The vertex is the highest or lowest point of the graph (x,y)
The optimal value is the y value. The y value can tell you if the graph is going upward or downward. The y value is either the minimum value or maximum value. If it is the minimum value, then the graph is direction of opening is upward if it is maximum then the graph direction of opening is downward.
The axis of symmetry is the x value. It tells were the graph is reflected.
x+h and ay+k
Finding X intercepts
- When finding the x-intercepts, plug 0 into y.
- Move k to the other side (don't forget to change the sign, positive or negative).
- Divide both sides with "a", completely canceling "a" on the side with the brackets. Leaving the brackets alone, "(x - h)^2".
- Square root both sides, completely canceling "^2" on the side with the brackets and getting rid of them, leaving you with "x - h".Solve by bringing over the number to leave the variable alone, and you have one of your x-intercepts.~ Solve again, but change the sign (positive/negative) of the number on the side with no variable and then solve, giving you your other x-intercept.