Write the equation of the quadratic function given the following

Question

1. Vertex (2,5) Point: (-1,3)

2. Vertex (2,-3) Point (4,1)

 

Answer 1

The standard form of a quadratic function is y=ax²+bx+c 

The vertex form of a quadratic function is y=a(x-h)²+k, where (h,k) are the coordinates of the vertex. 

 

Since you are given the vertex, that is the place to start.

1. Vertex (2,5) means you know y=a(x-2)²+5

    To find "a" use the point (-1,3). 

3=a(-1-2)²+5

3=a(-3)²+5  take away 5 from both sides

-2=a(9)  divide by 9 on both sides

-2/9 = a

So the quadratic is y=-2/9(x-2)²+5. You don't say if it can be given this way or if you need to bring it to standard form.  I am assuming you do, so you need to expand it out. Start by squaring.

y=-2/9(x²-4x+4)+5     Distribute the -2/9

y=-2/9x²+2/9x-4/9+5  Combine like terms

y=-2/9x2+2/9+41/9

 

2. y=a(x-2)²-3

   1=a(4-2)² -3

   4=a(2)²

   4=a(4)

   1=a

   so y=(x-2)² -3

  y=x²-4x+4-3

  y=x²-4x+1