Graphing Quadratic Functions and Transformations

What is the parent function of a quadratic function?

• y = x

• y = x^2

• y = x^3

• y = 1/x

What shape does the graph of y = x^2 form?

• Circular shape

• Inverted curve

• Straight line

• U-shaped curve

What does a negative coefficient in front of x^2 indicate about the graph's orientation?

• It shifts to the right

• It shifts to the left

• It opens upwards

• It opens downwards

What transformation does 'x - 3' inside the squared term represent?

• Shift up by 3 units

• Shift down by 3 units

• Shift right by 3 units

• Shift left by 3 units

What is the effect of a vertical stretch by a factor of 3 on the graph of a quadratic function?

• Shifts it downwards

• Shifts it upwards

• Makes it narrower

• Makes it wider

How does the transformation 'minus 5' outside the squared term affect the graph?

• Moves it 5 units up

• Moves it 5 units down

• Moves it 5 units left

• Moves it 5 units right

What is the domain of any quadratic function in vertex form?

• All negative numbers

• All non-zero numbers

• All real numbers

• All positive numbers

In vertex form, what does the 'k' value represent?

• Compression factor

• Stretch factor

• Vertical shift

• Horizontal shift

Which form of a quadratic function is most useful for solving equations?

• Expanded form

• Factored form

• Standard form

• Vertex form

What does the vertex form of a quadratic function allow you to easily identify?

• The intercepts on the graph

• The asymptotes of the function

• The maximum or minimum point

• The roots of the function