Find a possible formula for the quadratic fiction whose graph

Question

 

 

Find a possible formula for the quadratic function whose graph has  a vertex (6,3) and y intercept -4

Answer 1

The vertex form of a quadratic equation is:

 

     y = a(x-h)² + k

 

where (h,k) is the location of the vertex and "a" is a constant.  The problem gives you the location of the vertex as (6,3) so e can just plug them into the equation:

 

     y = a(x-6)² + 3

 

To find "a", plug in the known y-intercept, (0,-4), and solve for "a":

 

     -4 = a(0-6)² + 3

     -4 = 36a + 3

     -7 = 36a

     -7/36 = a

 

So the final equat6ion is:

 

     y = (-7/36)(x-6)² + 3

Answer 2

Hi Katherine,

y = a(x - h)² + k,    (h, k) = (6, 3)

y = a(x -6)² + 3,     y-intercpet has y = - 4, x=0

-4 = a(0-6)² +3

-7 = 36a, or a = -7/36

y=-7/36(x-6)² + 3