Dilations of Quadratic Equations

What are transformations in the context of quadratic functions?

• Changes to the graph, including translations, reflections, and dilations.

• The highest point on the graph.

• The lowest point on the graph.

• The set of all possible input values.

Which transformation involves stretching or compressing the graph?

• Dilation

• Translation

• Reflection

• Rotation

"a" causes the parabola to vertically ​ (a)   when a < 1.

• compress

• stretch

"a" causes the parabola to vertically ​ (a)   when a > 1.

• stretch

• compress

a

b

c

d

Vertical Dilation

Horizontal Dilation

Horizontal Translation

Vertical Translation

The graph shows the function f(x)=x² in blue and another function g(x) in red.  Which could be the equation for g(x)?

• g(x)=3x²

• g(x)=1/3x²

• g(x) = x² - 3

• g(x) = (x-3)²

Label how each number transforms the function

b

c

d

e

Left 3

Right 3

Moves up 7

Reflected over the x-axis

Stretched by a factor of 2

• compress

• stretch

The graph shows the function f(x)=x² in blue and another function g(x) in red.  Which could be the equation for g(x)?

• g(x) = 2x²

• g(x) = 1/2x²

• g(x) = x² + 2

• g(x) = (x + 2)²

The graph shows the function f(x)=x² in blue and another function g(x) in red.  Which could be the equation for g(x)?

• g(x)=3x²

• g(x)=1/3x²

• g(x) = x² - 3

• g(x) = (x-3)²