—  Standard
Form of a Quadratic Relation
◦  y = ax2 + bx + c, where the value of a tells you
the direction of opening of the parabola
(+ means up and – means down) and c is the
y-intercept.
—  Factored
Form of a Quadratic Relation
◦  y = a (x – s)(x – t), where the value of a tells
you the direction of opening of the parabola
(+ means up and – means down) and s and t are
the zeros (x-intercepts).
—  To
rewrite standard form in factored
form:
◦  Common factor.
◦  Factor the trinomial by finding the magic
numbers.
—  This
allows you to find the zeros of the
quadratic relation without creating a
table of values and graphing.
1. 
Write the following in factored form.
a)  y = x2 + 3x + 2
y = (x + 2)(x + 1)
b)  y = x2 – 8x – 20
y = (x – 10)(x + 2)
c)  y = 4x2 – 8x – 60
y = 4 (x2 – 2x – 15)
y = 4 (x – 5)(x + 3)
—  To
rewrite factored form in
standard form:
◦  Expand (multiply the a)
◦  Expand (FOIL)
◦  Simplify
—  This
allows you to find the
y-intercept without creating a table
of values and graphing.
1. 
Write the following in standard form.
a)  y = (x – 2)(x – 8)
y = x2 – 8x – 2x + 16
y = x2 – 10x + 16
b)  y = 4 (x – 6)(x – 1)
y = (4x – 24)(x – 1)
y = 4x2 – 4x – 24x + 24
c)  y = -3 (x + 5)(x – 2)
y = (-3x – 15)(x – 2)
y = -3x2 + 6x – 15x + 30
y = -3x2 – 9x + 30