Introduction to Quadratics

Which transformation transforms the graph of

f(x) = x² to the graph of

g(x) = (x + 4)²?

• a vertical shift 4 units up

• a vertical shift 4 units down

• a horizontal shift 4 units to the left

• a horizontal shift 4 units to the right

How did we transform from f(x) =x²

to

g(x) = -3x²

• reflection over x-axis and vertical shift down 3 units.

• reflection over x-axis and vertical stretch by a factor of 3.

• horizontal stretch by a factor of 3.

• reflection over x-axis and vertical compression by a factor of 3.

How did we transform from the parent function?

g(x) = -1/5(x - 1)² + 7

• reflection across the x-axis, vertical compression by a factor of 1/5, horizontal shift right 1, vertical shift up 7.

• vertical compression by a factor of 1/5, horizontal shift left 1, vertical shift up 7

• reflection across the x-axis, horizontal shift right 1, vertical shift down 7

• no changes were made to y = x²

Which transformation transforms the graph of

f(x) = x² to the graph of

g(x)=5(x+3)²-10?

• Vertical stretch by a factor of 5, right 3, down 10.

• Vertical stretch by a factor of 5, left 3, down 10.

• Reflect across the x-axis, vertical stretch by a factor of 3, up 5, left 10.

• Horizontal stretch by a factor of 5, left 3, down 10.

Which transformation transforms the graph of

f(x) = x² to the graph of

g(x) = -(x + 3)² - 5?

• left 5, up 3, reflect across the x-axis

• reflect across the x-axis, left 3, down 5.

• Left 3, vertical stretch by a factor of 5,

• Reflect across the x-axis, right 3, down 5

Which transformation transforms the graph of

f(x) = x² to the graph of

g(x) = 3/4 (x - 5)² + 12 ?

• reflection by a factor of 34

• left 5, up 12, and a horizontal compression by a factor of 3/4

• Vertical compression by a factor of 3/4, right 5, and up 12

Which transformation transforms the graph of

f(x) = x² to the graph of

gf(x) = -x ² -11

• Down 11 and reflected across the x-axis.

• Reflect across the y-axis and up 11.

• down 11

• up 11

Which transformation transforms the graph of

f(x) = x² to the graph of

g(x) = -2 (x +10)² ?

• Reflect across the x-axis, vertical stretch by a factor of 2, right10.

• Reflect across the x-axis and left 10.

• Reflect across the x-axis, vertical stretch by a factor of 2, up 10.

• Reflect across the x-axis, vertical stretch by a factor of 2, left 10.

Which transformation transforms the graph of

f(x) = x² across the x-axis, left 3 and down 5.

• g(x) = -(x + 3)² - 5

• g(x) = (x - 3)² - 5

• f(x) = -(x + 5)² + 3

What is the axis of symmetry in the function f(x) = (x-1)² +2

• x = 1

• x = -1

• x = 2

• x = -2