Transcript Roots, Standard, and Vertex

Review for Quiz 1
Roots, Standard, and Vertex
3 Forms of the Quadratic Function
The graph of a quadratic function is a
parabola.
Standard Form
f ( x)  x  6 x  8
2
Root Form
8
6
f ( x)  ( x  4)( x  2)
4
Vertex Form
f ( x)  ( x  3)  1
2
2
5
f ( x)  x  6 x  8
a  1 b  6 c  8
2
b
x
2a
Standard Form
• Best for
(6)
x
 3 identifying the y2(1)
intercept.
(0,8)
Now plug this x back into the original.
f (3)  (3)  6(3)  8
f (3)  9  18  8
f (3)  9  8
(3, 1)
f (3)  1
2
Vertex
• Also know as
polynomial form
or a,b,c form.
• To find the vertex
use …
f ( x)  ( x  4)( x  2)
Root Form
Roots. Just change the signs.
x  {4, 2}
y – intercept. Just multiply
the two roots together.
f (0)  (0  4)(0  2)
 (4)(2)
8
(0,8)
• Great for finding the
zeros of an equation.
• Also known as factored
form.
• To find the
y-intercept…
f ( x)  ( x  3)  1
2
Vertex. Just change the sign of the number
with the x. Keep the other sign
(3, 1)
Find the zeros.
0  ( x  3)  1
2
1  ( x  3)
2
 1  ( x  3)
1  x  3
3 1  x
2
Vertex Form
• Best for identifying
the vertex.
• Great for graphing by
hand equation.
• To find the zeros set
it equal to zero and
solve for x.
x  {4, 2}
Is this easier
than
factoring?
3 Forms of Quadratic Functions
Standard
y  ax 2  bx  c
Ex.
0  x2  6 x  8
Pros.
y – int (0, c)
To find
roots
Vertex
Root/Intersect/Factored Vertex
y  a( x  r1 )( x  r2 )
y  a ( x  h) 2  k
0  ( x  2)( x  4)
Roots
x  {r1, r2 }
1. Factor
2. Set each
factor = 0
1. Set each
factor = 0
 b

 , Pin 
 2a

 r1  r2

,
Pin


2


0  ( x  3)2  1
Vertex (h, k)
1. Set = 0
2. Solve by
square roots.
 h, k 