Parabola Translations

QUADRATICS
&
Parabolas

FEATURES OF A

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Multiple Choice

Which graph is a parabola?

Multiple Choice

Name the x-intercept(s)?

• (0, 0)
• (2, 4)
• (0, 0) and (0, 4)
• (0, 0) and (4, 0)

Multiple Choice

What is the vertex of the graph?

• (2, 4)
• (3, -1)
• (0, 8)
• (4, 2)

Multiple Choice

Is this point a max or min?

• max
• min

Multiple Choice

What is the equation for axis of symmetry?

• y=3
• x=3
• x=5
• x=1

Multiple Choice

What is the significance of the ordered pair (2, -4) to the graph?

• It is the vertex

• It is an x-intercept

• It is the y-intercept

• It is the axis of symmetry

Dilations

Dilation has the effect of stretching or compressing a graph

Reflections

Multiple Choice

Is this parabola a stretch or a shrink?

• Stretch

• Shrink

Multiple Choice

Which equation will result in the parabola being a narrower graph?

• y = 2x² + 1

• y = 7x² - 1

• y = 0.5x² + 1

• y = x²

Multiple Choice

Which equation would result in the parabola being wider?

• y = 0.5x² + 2

• y = x²

• y = 10x² + 7

• y = - 3x² - 2

Multiple Choice

Which best describes this parabola?

• Stretch/Non-reflection

• Shrink/Non-reflection

• Stretch/Reflection

• Shrink/Reflection

Multiple Choice

Is this parabola a reflection or non-reflection?

• Reflection

• Non-reflection

Multiple Choice

Is this parabola a reflection or a non-reflection?

• Reflection

• Non-reflection

Multiple Choice

What is the correct graph for the equation y = - 0.5x² + 2

Translations

A TRANSLATION IS THE MOVEMENT
OF EVERY POINT ON AN OBJECT AT
THE SAME DISTANCE IN THE SAME DIRECTION - VERTICAL OR HORIZONTAL

TURNING POINT FORM

When a quadratic is in this form, it is
easiest to determine the translations

The turning point has the coordinates (h, k)

h represents the number of units that y=x² is translated horizontally

k represents the number of units that y=x² is translated vertically

EXAMPLES

Multiple Choice

Which transformation maps the graph of
f(x) = x² to the graph of g(x) = (x + 4)²?

• a reflection across the line x = -4
• a reflection across the line y = -4
• a translation shifting f(x) 4 units to the left
• a translation shifting f(x) 4 units to the right

Multiple Choice

How would you describe the transformation from $$y=x^2$$ to $$y=x^2-7$$

• Vertical translation 7 units down

• Vertical translation 7 units up

• Horizontal translation 7 units left

• Horizontal translation 7 units right

Multiple Choice

What steps transform the graph y = x² to y = x² + 8

• shifted up 8 units

• shifted down 8 units

• shifted left 8 units

• shifted right 8 units

Multiple Choice

How did we transform from the parent function?
y = x² + 2

• horizontal shift up
• vertical shift up
• horizontal shift down
• vertical shift down

EXAMPLES

Multiple Choice

What steps transform the graph y = x² to y = (x - 4)²

• Shifted down 4 units

• Shifted left 4 units

• Shifted right 4 units

• Shifted up 4 units

Multiple Choice

What steps transform the graph y = x² to y = (x-4)²

• Shifted down 4 units

• Shifted left 4 units

• Shifted right 4 units

• Shifted up 4 units

Multiple Choice

Given f(x) = (x + 3)² , how did we transform from the parent function?

• Horizontal shift left 3

• Vertical shift up 3

• Horizontal shift right 3

• Vertical shift down 3

TURNING POINT FORM

Multiple Choice

What is the vertex of the following function: $$y=\left(x-4\right)^2+1$$

• (-4 , 1)

• (-4 , -1)

• (4 , -1)

• (4 , 1)

Multiple Choice

Match the equation to its description.

• Right 2 and up 2
• Left 2 and up 2
• Right 2 and down 2
• Left 2 and down 2

Multiple Choice

How would you describe the transformation from $$y=x^2$$ to $$y=\left(x-2\right)^2+4$$

• Vertically translated 2 units down and horizontally translated 4 units right

• Vertically translated 4 units down and horizontally translated 2 units left

• Vertically translated 2 units down and horizontally translated 4 units left

• Vertically translated 4 units up and horizontally translated 2 units right

Multiple Choice

What is the function of the graph?

• $$y=\left(x-2\right)^2+3$$

• $$y=\left(x-3\right)^2+2$$

• $$y=\left(x+3\right)^2+2$$

• $$y=\left(x+3\right)^2-2$$

Multiple Choice

What is the function of the graph?

• $$y=\left(x-2\right)^2$$

• $$y=\left(x+2\right)^2$$

• $$y=x^2-2$$

• $$y=x^2+2$$