Vertex Form of a quadratic equation
A quadratic equation has the vertex form:
[tex]y=a(x-h)^2+k[/tex]
Where (h,k) is the vertex of the parabola and a is the leading coefficient.
If a is positive, the parabola is concave up, if a is negative, the parabola is concave down.
We'll identify each graph with a number so we can relate them with their corresponding equation.
Graph 1. Has the vertex at (-5,7) and opens up. The equation of this parabola (for a=1) is:
[tex]y=(x+5)^2+7[/tex]
Graph 2 has the vertex at (5,7) and opens up. The equation is:
[tex]y=(x-5)^2+7[/tex]
Graph 3 has the vertex at (5,-7) and opens up. The equation is
[tex]y=(x-5)^2-7[/tex]
Graph 4 has the vertex at (5,-7) and opens down. The equation is
[tex]y=-(x-5)^2-7[/tex]
Graph 5 has the vertex at (-5,-7) and opens up. The equation is
[tex]y=(x+5)^2-7[/tex]
Finally, graph 6 has the same vertex as graph 5 and opens up also, but it grows much faster than that one. The difference is that the leading factor is greater than one. This corresponds to the equation
[tex]y=6(x+5)^2-7[/tex]
The image below shows the correspondence between the graphs and their equations labeled with numbers.
