Exploring Transformations of A and C

What is the standard form of a quadratic parent function?

• y = x^2

• y = x^3

• y = 2x + 1

• y = x + 2

When graphing by hand, what is the y-value when x is -1?

• 0

• 1

• -1

• 2

What effect does changing the coefficient 'a' to 4 have on the quadratic graph?

• Shifts it up

• Makes it narrower

• Shifts it down

• Makes it wider

What happens to the graph of a quadratic function if the coefficient 'a' is negative?

• It becomes wider

• It shifts to the right

• It opens upwards

• It flips downwards

Using the running analogy, what does a larger 'a' value signify about the graph's width?

• No change to the graph

• Graph shifts upwards

• Graph becomes narrower

• Graph becomes wider

What is the effect of a positive 'a' value greater than 1 on the quadratic graph?

• Graph opens downwards

• Graph becomes wider

• Graph becomes narrower

• Graph shifts to the left

How does a negative 'a' value affect the direction of a quadratic graph?

• Opens upwards

• Shifts to the left

• Opens downwards

• Shifts to the right

What does the coefficient 'c' primarily affect in a quadratic graph?

• Width of the graph

• Horizontal shift

• Direction it opens

• Vertical shift

If the coefficient 'c' is -4, where will the graph's vertex be located?

• At (-4, 0)

• At (0, 4)

• At (0, -4)

• At (4, 0)

What does a 'c' value of 0 imply about the position of the quadratic graph?

• Touches the x-axis

• Touches the y-axis at y=0

• Is located at the origin

• Shifts 4 units up