A2 – Section 4.8
Date____________
Quadratic Formula
The quadratic formula allows you to find a solution to any quadratic equation that is in
standard form, ______________________.
Quadratic Formula: x 
 b  b 2  4ac
, given ___________________ and ______
2a
Ex 1 Simplify the following expressions.
a)
24 3
6
b)
4  12
10
c)
6  18
12
To use the quadratic formula:
1.
2.
3.
4.
Set the equation equal to ____________.
Find values for ______, ______ and ______.
___________ a, b, and c into the quadratic formula using _____________.
Simplify using ________________________________.
Ex 2 Solve.
a = _____
b = _____
c = _____
3x2 + 8x = 35
Ex 3 Solve.
a) 12x – 5 = 2x2 + 13
b) -2x2 = -2x + 3
a)__________________
b)___________________
Discriminant = _______________



The discriminant tells you the type of solutions, _______ or ____________
The discriminant tells you how many solutions there are to any quadratic equation.
Interpretations of the discriminant will be one of the following: 2 real solutions,
1 real solution, or 2 complex solutions
Using the Discriminant of ax2 + bx + c = 0
Value of the
discriminant
Number and Type
of Solutions
The Graph of
y = ax2 + bx + c
b2 – 4ac > 0
b2 – 4ac = 0
b2 – 4ac < 0
Ex 4 Tell the nature of the roots of the following quadratic equations.
a)
y = 4x2 + 3x + 9
b)
y = 3x2 – 10x
c)
y = 8x2 – 1
Disc:____ Roots:________
Disc:____ Roots:________
Disc:____ Roots:________