vertex (3,-3) points (2,-1)

Question

determine the quadratic function with vertex(3,-3) and points (2,-1)

Answer 1

Let's use the following form of the quadratic equation since you have the vertex: y = a(x - h)² + k

 

 

The vertex tells us h and k in the equation.  The point will allow us to find a.

 

 

 

Use the information given for the vertex: y = a(x - 3)² + (-3) = a(x - 3)² - 3

 

 

 

Now use (2, -1) for x and y to find a:

 

-1 = a(2 - 3)² - 3

 

-1 = a - 3

 

a = 2

 

 

The quadratic equation is y = 2(x - 3)² - 3.

 

 

You can expand the square to get y = 2(x² - 6x + 9) - 3 = 6x² - 12x + 15.