4­7 Quadratics in Vertex Form Day One
November 3, 2014
4.7 ­ Quadratic Functions in Vertex Form
Quadratic: Has the parent function y = x2.
Parabola: A U­shaped graph.
y = x2
X
Y
­3
9
Because the vertex is translated h horizontal units and k vertical from the origin, the vertex of the parabola is at (h, k).
­2
­1
0
1
2
3
Shift Function Notation h positive: right
h negative: left
k positive: up
k negative: down
a > 1 stretch Away from x ­
axis
0 < a < 1 compress toward x ­
axis
b > 1: stretch away from y ­
axis
0 < b < 1: compress towards y
­ axis
Reflect over y ­ axis
Reflect over x ­ axis
a +: Opens Up
a ­: Opens Down
1
4­7 Quadratics in Vertex Form Day One
Use the graph of f(x) = x2 as a guide, describe the transformations and then graph each function.
1.
g(x) = (x – 2)2 + 4
3.
1 x2
g(x) =­ 4
2.
g(x) = (x + 2)2 – 3
4.
g(x) =(3x)2
November 3, 2014
5. Use the description to write the quadratic function in vertex form.
Vertex Form:
The parent function f(x) = x2 is vertically stretched by a factor of 4/3 and then translated 2 units left and 5 units down to create g.
h:
k:
a:
6. Use the description to write the quadratic function in vertex form.
The parent function f(x) = x2 is vertically stretched by a factor of 4, reflected across the x ­ axis and then translated 3 units right and 9 units up to create g.
Vertex Form:
h:
k:
a:
2