Quadratic Functions Transformation

What is the axis of symmetry?

• the slope of the graph

• the dividing line for a parabola

• a way to spin my pencil

• the x-axis

Find the axis of symmetry for f(x) = x² + 4x - 5 

Graph the equation

• x = 2

• x = -2

• x = 4

• x = -4

Describe the transformations of f(x)=x² to the graph of
g(x)=x²+5.

• horizontal shift right 5 units

• horizontal shift left 5 units

• vertical shift up 5 units

• vertical shift down 5 units

What is the range of the graph?

Hint: Use the minimum or maximum

• All real numbers

• To infinity and beyond

• y ≥ -1

• x ≥ 0

Tags

CCSS.8.F.A.1

CCSS.HSF.IF.B.5

Does this graph in the back have maximum or minimum value?

• maximum

• minimum

• neither

• both

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

Which of the following describes the transformations done to the quadratic parent function of f(x) = x² to obtain g(x) = 2x² + 4 ?

• Vertical Stretch by a factor of 2 and vertical shift up 4 units

• Vertical Compress by a factor 2 and vertical shift up 4

• Vertical Stretch by a factor of 2 and horizontal shift left 4 units

• Vertical Compress by a factor of 2 and horizontal shift right 4 units

What is the equation of the quadratic function obtained from vertically compressing the parent function by a factor of 0.5 and then reflecting across the x-axis?

• f(x)= 0.5x²

• f(x)= -0.5x²

• f(x)= -(x-0.5)²

• f(x)= x²+0.5

What would the equation for the new quadratic function be if it was horizontally shifted right 1 unit  from the function f(x)=x²+4?

• g(x)=x²+5

• g(x)=(x+1)²+4

• g(x)=(x-1)²+4

• g(x)=x²+3

What is the horizontal shift of this equation?
y = -(x + 3)² - 5

• left 3

• right 3

• left 5

• right 5