1. Lesson 6.3 Interpreting Vertex Form & Standard Form
PLEASE TEAR OUT YOUR 6.3 PACKET, PAGES

2. What is Standard Form? 𝑓 𝑥 =𝑎 𝑥 2 +𝑏𝑥+𝑐
Things to know about standard form:
In order for a function to be quadratic, it MUST have an 𝑥 2 term!
Vertex = (− 𝑏 2𝑎 , 𝑓 − 𝑏 2𝑎 )
Axis of Symmetry = x coordinate of vertex
Maximum (if graph opens down) or Minimum (if graph opens up) = y coordinate of vertex

3. Example 1 – Identifying a Quadratic Function
Remember, if it is a quadratic function, there must be an x-squared term!
Determine if the equation is a quadratic function. If so, give the axis of symmetry and the coordinate of the vertex. 𝑦=
b) 𝑥+2=4𝑥+3
a) 𝑦=2𝑥+5 𝑥 2 +3
No, not quadratic.
Yes, quadratic. 𝑦=
Vertex: (− 𝑏 2𝑎 , 𝑓 − 𝑏 2𝑎 )
c) 𝑦−3=2 𝑥 2
Yes, quadratic.
− 𝑏 2𝑎 =− =− 2 10 =− 1 5 𝑦=
Vertex: (− 𝑏 2𝑎 , 𝑓 − 𝑏 2𝑎 )
𝑦=5( 1 5 )
𝑦= 18 5
− 𝑏 2𝑎 =− =0
vertex:(0, 3)
axis of symmetry:x=0
𝑣𝑒𝑟𝑡𝑒𝑥=(− 1 5 , 18 5 )
𝑦=2(0 ) 2 +3
𝑦=5( 1 25 )
𝑦=3
𝑎𝑥𝑖𝑠 𝑜𝑓 𝑠𝑦𝑚𝑚𝑒𝑡𝑟𝑦; 𝑥=− 1 5

4. Example 2 – Changing from Vertex to Standard Form
Just multiply it all out!
a) 𝑦=2(𝑥+5 ) 2 +3
b) 𝑦=−3(𝑥−2 ) 2 −4
𝑦=2(𝑥+5)(𝑥+5)+3
𝑦=−3 𝑥−2 𝑥−2 −4
𝑦=2( 𝑥 2 +10𝑥+25)+3
𝑦=−3 𝑥 2 −4𝑥+4 −4
𝑦= 2𝑥 2 +20𝑥+50+3
𝑦= −3 𝑥 2 +12𝑥−12 −4
𝑦= 2𝑥 2 +20𝑥+53
𝑦= −3𝑥 2 +12𝑥−16

5. Example 3 – Writing a Quadratic Function Given a Table of Values
Steps:
1) Identify the vertex (h,k)
2) Plug in another point with the vertex into vertex form to find a.
3) Write the function in vertex form
4) Convert to standard form.
Vertex =(−3, 0)
Rewrite in Standard Form:
y=(𝑥+3 ) 2
Point =(0, 9)
Vertex Form: 9=𝑎(0+3 ) 2
y=(𝑥+3)(𝑥+3)
9=𝑎(3 ) 2
9=9𝑎
y= 𝑥 2 +6𝑥+9
1=𝑎 x y -6 9 -4 1 -3 -2
y=(𝑥+3 ) 2

6. Example 4 – Writing a Quadratic Function Given a Table of Values
Vertex =(−2, −3) x y 13 -1 1 -2 -3 -4
Rewrite in Standard Form:
y=4(𝑥+2 ) 2 −3
Point =(−1, 1)
y=4 𝑥+2 𝑥+2 −3
Vertex Form: 1=𝑎(−1+2 ) 2 −3
y= 4(𝑥 2 +4𝑥+4)−3
1=𝑎(1 ) 2 −3
y= 4𝑥 2 +16𝑥+16−3
1=𝑎−3
4=𝑎
y= 4𝑥 2 +16𝑥+13
y=4(𝑥+2 ) 2 −3

7. Example 5 – Writing a Quadratic Function from a Graph
Use the graph to find an equation for 𝑓(𝑡)
Find the vertex:
(0, 25)
Point:
(1, 9)
Plug into vertex form:
9=𝑎(1−0 ) 2 +25
9=𝑎(1 ) 2 +25
9=𝑎+25
−16=𝑎
𝑓 𝑡 =−16 𝑥 2 +25

8. Example 6 – Writing a Quadratic Function from a Graph
Use the graph to find an equation for 𝑓(𝑡)
Find the vertex:
(0, 40)
Point:
(1, 24)
Plug into vertex form:
24=𝑎(1−0 ) 2 +40
24=𝑎(1 ) 2 +40
24=𝑎+40
−16=𝑎
𝑓 𝑡 =−16 𝑥 2 +40

9. Assignment #32
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