Quadratics
Part 1 
y
= a(x
 h)^{2}
+ k 
Enter a
= 1,
h = 0, k = 0
gives
y = 1(x  0)^{2} + 0 or y = x^{2}

Click Graph, then Click Store.
Use this graph to compare 
1 . Enter a
= 1,
h = 0, k =
2

Predict
which way the graph will SHIFT? 

Now click Graph. 
2. Enter a
= 1,
h = 0, k =
2

Predict
which way the graph will SHIFT? 

Now click Graph. 
3. Enter a
= 1,
h = 0, k =
3/2

Predict
which way the graph will SHIFT? 

Now click Graph. 
Quadratics
Part 2 
y
= a(x
 h)^{2}
+ k 
Enter a
= 1,
h = 0, k = 0
gives
y = 1(x  0)^{2} + 0 or y = x^{2}

Click Graph, then Click Store.
Use this graph to compare 
1 . Enter a
= 1,
h = 2, k =
0

Predict
which way the graph will SHIFT? 

Now click Graph. 
2. Enter a
= 1,
h = 2, k =
0

Predict
which way the graph will SHIFT? 

Now click Graph. 
3. Enter a
= 1,
h = 4/3, k =
0

Predict
which way the graph will SHIFT? 

Now click Graph. 
Quadratics
Quick Quiz 
Without
graphing predict which way the graph will shift from y = x^{2} 
1. y
= (x + 2)^{2}

Predict
which way the graph will SHIFT? 

Verify
with grapher 
2. y
= x^{2}
+ 3 
Predict
which way the graph will SHIFT? 

Verify
with grapher 
3. y
= (x  3)^{2}

Predict
which way the graph will SHIFT? 

Verify
with grapher 
4. y
= x^{2}  1 
Predict
which way the graph will SHIFT? 

Verify
with grapher 
Quadratics
Part 3 
y
= a(x
 h)^{2}
+ k 
Enter a
= 1,
h = 0, k = 0
gives
y = 1(x  0)^{2} + 0 or y = x^{2}

Click Graph, then Click Store.
Use this graph to compare 
1 . Enter a
= 1/2,
h = 0, k =
0

Predict
which way the graph will CHANGE? 

Now click Graph. 
2. Enter a
= 2,
h = 0, k =
0

Predict
which way the graph will CHANGE? 

Now click Graph. 
3. Enter a
= 1,
h = 0, k =
0

Predict
which way the graph will CHANGE? 

Now click Graph. 
4. Enter a
= 1/10,
h = 0, k =
0

Predict
which way the graph will CHANGE? 

Now click Graph. 
5. Enter a
= 4,
h = 0, k =
0

Predict
which way the graph will CHANGE? 

Now click Graph. 
Quadratics
Altogether 
Predict
the following shifting, then verify using grapher. 
y
= 2(x  3)^{2}
+ 4 
y
= 2(x + 3)^{2}
 4 
y
= 1/4(x + 2)^{2}
+ 1 
y
= 4(x  1)^{2}
 2 
y
= (x  2/5)^{2}
 1/5 

Quadratics
Part 4 
y
= a(x
 h)^{2}
+ k 
The
vertex is the point (h,k) 
If
a > 0 , then the vertex is the lowest point of the graph.
(opens upward) 
If
a < 0 , then the vertex is the highest point of the graph.
(opens downward) 
Examples: 
Quadratic 
Vertex 
y
= (x  1/2)^{2}
+ 3/5 
(1/2,
3/5) 
y
= 2 (x + 3)^{2}
 4 
(3,4) 
y
= 3(x + 1)^{2}

(1,0) 
y
= 2x^{2}
 4 
(0,4) 
y
= 2 (x  3)^{2}
+ 4 
(3,4) 