whats 1,3 in a parabola equation

Question

whats 1,3 in a parabola equation

Answer 1

Are you asking what parabola passes through the point (1,3)?  There are infinitely many.  One example would be:

 

     y = 3x²

 

When you plug in x=1, you get y = 3*(1²) = 3.  In general, you can use the vertex form of a quadratic equation (parabola) to find a parabola that passes through a given point such as (1,3):

 

     y = a(x-h)² + k

 

Where (h,k) is the position of the vertex and a is a constant.  Let's put the vertex at (h,k) = (-2, -6). Since we want to parabola to pass though the point (1,3), set (x,y) = (1,3) and solve for a:

 

     3 = a(1+2)² + 6

     3 = 9a - 6

     9 = 9a

     1 = a

 

So the parabola with its vertex at (-2,-6) that passes through the point  (1,3) is:

 

     y = (x+2)² - 6 = x² + 4x - 2