Writing Quadratic Equations When Given the Vertex and a Point
When writing quadratic equations, one very important point is the vertex.
The vertex helps to identify the horizontal and vertical translations.

We must know one other point in order to
identify the vertical stretch

Having the vertex and one other point is
enough information to create a quadratic
function
(3,2)
(5,10)
(3,2)
Example
Write a quadratic function given the vertex and another point:
Vertex (-2,1)
Point (5,4)
Method 1
 Sketch graph
 Identify HT, VT & VS
 Write equation in transformational form
HT=-2
VT=1
VS=3/49
Equation:
49/3(y-1)=(x+2)2
Method 2
Vertex (-2,1)


Point (5,4)
Fill Vertex and Point into Transformational form of equation
Solve for coefficient of “y” (will be reciprocal of VS)
Fill in point (5,4)
A(y-k)=(x-h)2
A(y-1)=(x+2)2
A(4-1)=(5+2)2
3A = 72
3A = 49
A = 49/3
THUS, Equation:
49/3(y-1)=(x+2)2