Factored Form of a Quadratic Relation
 When a quadratic relation is expressed in factored form y = a(x – r)(x – s),
 the zeros (x-intercepts ) are r and s
 the equation of the axis of symmetry
rs
is the vertical line defined by x 
2
rs
 the x-coordinate of the vertex is
2
 the y-coordinate of the vertex can
be found by substituting the x-coordinate
of the vertex into the equation
x
rs
2
Example 1
For each quadratic relation,
i) determine the y-intercept
ii) determine the zeros
iii) determine the equation of the axis of symmetry
iv) determine the coordinates of the vertex
v) sketch the graph
a) y = 2(x + 3)(x – 1)
b) y = -x(x – 4)
c) y = (x + 2)2
x
rs
2
An equation of a quadratic relation can be found using the zeros and the coordinates
of one other point on the parabola.
Example 2
Determine the equation (in factored form) of the quadratic relation.
a) the parabola has x-intercepts -1 and 6 and y-intercept -12
b) the parabola has zeros -5 and -3 and a minimum value of 7
c)