The Quadratic
Formula
y =
2
ax
+ bx + c
(Standard Form)
* To apply the formula, you must write
the equation in standard form first!
x2+5x = 14 (not in standard form)
-14 -14
x2+5x-14 = 0 (This is standard form.)
This gives us the x-intercepts
Quadratic Equation:
x  b  b  4ac
2a
2
 (5)  5  41 14
x
2 1
x2+5x-14 = 0
2
 5  25  56

2
 5  81

2
59
59
59



2
2
2
2
x = 2,-7
7
To graph, find the vertex
b
x
2a
5
x
2
5
Plug  back in for y.
2
x  5 x  14  y
2
5 2
5
(( ) )  5(( ) )  14  y
2
2
25 25
  14  y
4
2
25 50
  14  y
4
4
Y value is
81
 y
4
 25 56 Change -14 to ¼’s

4
4
5 81
Vertex is ( , )
2 4
To graph, make mixed numbers
1
1
(2 ,20 )
2 y 4
1
2
2
-7
2
 20
1
4
x
Practice saying the
Quadratic Equation…
Sing along with the clip!
Solve:
0  x  2x  5
2
Clear out - in front of a by
multiplying both sides by -1
0=
2
x +2x-5
 b  b  4ac
x
2a
2
2
2  4(1)( 5)

2(1)
 2  4  20

2
2
2
24

2
 2  24
 2  24

AND

2
2
Use calculator
≈1.45
to find exact 3.45
Find Vertex and Graph
b
2
x
y  (1)  2(1)  5
2a
 (2)


1

2

5
x
2(1)
2
x
2
6
 1
Vertex (-1,6)
6
-4 -3
Why does it
open down?
-1
y
1
2
x
The original
was a negative!
REAL LIFE:
1050 ft.
If you throw a
rock straight
down from a cliff
at a speed of
30ft./sec., how
soon will it hit the
ground?
Formula: h=-16t2+vt+s
h= height at time t
t= time in seconds
s= starting height in feet
v= velocity (ft/sec.) falling is Set h=0 when rock hits ground
2
0=-16t +vt+s
2
0=-16t +(-30)t+1050
 (30)  (30)  4(16)(1050)
t
2(16)
2
30  68100

 32
30  68100 And 30  68100


 32
 32
 9.09
 7.22
 7 sec .
Can’t have - seconds