Exploring Quadratic Transformations: Shifts and Effects

What does the second difference being constant indicate about a sequence?

• It's a cubic sequence.

• It's an exponential sequence.

• It's a quadratic sequence.

• It's a linear sequence.

How do you determine the 'c' value in a quadratic equation?

• By finding the first difference.

• By solving for 'b'.

• By identifying the y-intercept.

• By calculating the second difference.

What does a negative 'b' value indicate about a quadratic equation?

• The parabola shifts to the left.

• The vertex is on the positive x-axis.

• The parabola opens downwards.

• The parabola shifts to the right.

How does a positive 'c' value in (x + c)^2 affect the parabola's position?

• Shifts it up.

• Shifts it right.

• Shifts it down.

• Shifts it left.

What does an equation of the form x^2 + d indicate about the parabola's shift?

• Shifts up by d units.

• Shifts down by d units.

• Shifts right by d units.

• Shifts left by d units.

If a parabola has an equation of x^2 - 4, how many units does it shift vertically?

• 4 units right

• 4 units left

• 4 units down

• 4 units up

What does the equation x^2 + 3 indicate about the parabola's shift?

• 3 units down

• 3 units up

• 3 units right

• 3 units left

How does the equation x - 5^2 indicate the direction of the parabola's shift?

• 5 units down

• 5 units left

• 5 units up

• 5 units right

In the equation G(x) = x + 3^2, how many units does the parabola shift horizontally?

• 3 units left

• 3 units down

• 3 units right

• 3 units up

What does a vertical shift of 4 units down in a parabola's equation look like?

• x + 4^2

• x^2 - 4

• x - 4^2

• x^2 + 4