Question

in the some important for of the image below about , some have more details available when you click on them Drag and drop each corresponding area it identities in the image

Answer 1

Vertex Form of a quadratic equation

A quadratic equation has the vertex form:

`y=a(x-h)^2+k`

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:

`y=(x+5)^2+7`

Graph 2 has the vertex at (5,7) and opens up. The equation is:

`y=(x-5)^2+7`

Graph 3 has the vertex at (5,-7) and opens up. The equation is

`y=(x-5)^2-7`

Graph 4 has the vertex at (5,-7) and opens down. The equation is

`y=-(x-5)^2-7`

Graph 5 has the vertex at (-5,-7) and opens up. The equation is

`y=(x+5)^2-7`

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

`y=6(x+5)^2-7`

The image below shows the correspondence between the graphs and their equations labeled with numbers.