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


The Quadratic Formula and the
Discriminant
2
b
 determines
– 4ac
how many and what type of
solutions a quadratic has.
1. x2 – 6x + 10 = 0
1.
2.
3.
Put the equation into standard form
Identify a, b, and c
Substitute into the quadratic equation
and simplify
b  b  4ac
x
2a
2
3. 4x2 + 8x = x2 + 35
A ball is thrown downward from a height of 6 feet
with an initial velocity of 32 ft/sec. If the ball is
caught at a height of 2 feet, for how long is the
ball in the air?
Concept Summary: Solving Quadratic Equations
Method
Graphing
Factoring
Square Root Property
Completing the Square
Quadratic Formula
Can be Used
When to use it…
Question
#
a
b
21
33
2 irrational
22
4
2 rational
23
49
2 rational
24
121
2 rational
25
-87
2 Complex
26
-40
2 Complex
27
36
2 rational
28
0
1 rational
29
1
2 rational
c
.5,1
3
h
h
= -16t2 + vot + ho
= ending height (feet)
 t = time (seconds)
 vo = initial velocity (feet per second)
 ho = initial height (feet)

If the measure of one side of a square is increased by 2
centimeters and the measure of the adjacent side is decreased by
2 centimeters, the area of the resulting rectangle is 32 square
centimeters. Find the measure of one side of the square.

A rock is thrown from the top of a tall building. The distance, in
feet, between the rock and the ground t seconds after it is thrown
is given by d = -16t2 – 4t + 382. How long after the rock is thrown
is it 370 feet from the ground?
Exit slip time