Exploring Quadratic Functions

What is the vertex of the parabola defined by the equation y = (x-3)^2 - 4?

• (3, -4)

• (-3 4)

• (0, 3)

• (3, 0)

Determine the axis of symmetry for the quadratic function y = (x + 3)x^2 + 8.

• x = 0

• x = 2

• x = -3

• x =8

Analyze the behavior of the graph of the function y = -3(x + 1)^2 + 2 as x approaches positive infinity.

• y approaches zero as x approaches positive infinity.

• y approaches negative infinity as x approaches positive infinity.

• y approaches positive infinity as x approaches positive infinity.

• y remains constant as x approaches positive infinity.

Classify the direction of the graph for the function y = -x^2 + 5.

• The graph opens downwards.

• The graph opens upwards.

• The graph is horizontal.

• The graph is a straight line.

If the vertex of a parabola is at (2, -3), what is the axis of symmetry?

• x = 2

• x = -2

• y = 2

• y = -3

Translate the function y = x^2 to the right by 3 units. What is the new equation?

• y = (x + 3)^2

• y = (x - 1)^2

• y = (x - 3)^2

• y = x^2 + 3

What is the vertex of the parabola represented by the equation y = (x - 5)^2 + 1?

• (5, 1)

• (1, 5)

• (2, 1)

• (0, 5)

How does the graph of y = x^2 change when it is translated down by 4 units?

• The graph of y = x^2 remains unchanged.

• The graph of y = x^2 translates to y = x^2 - 4.

• The graph of y = x^2 translates to y = -x^2.

• The graph of y = x^2 translates to y = x^2 + 4.

What is the behavior of the graph of y = 5(x - 2)^2 + 1 as x approaches negative infinity?

• The graph approaches positive infinity as x approaches negative infinity.

• The graph approaches negative infinity as x approaches negative infinity.

• The graph remains constant at y = 1 as x approaches negative infinity.

• The graph approaches zero as x approaches negative infinity.

Describe the behavior of the graph of y = 2(x + 2)^2 - 5 as x increases.

• The graph of y = 2(x + 2)^2 - 5 decreases as x increases.

• The graph of y = 2(x + 2)^2 - 5 remains constant as x increases.

• The graph of y = 2(x + 2)^2 - 5 oscillates as x increases.

• The graph of y = 2(x + 2)^2 - 5 increases as x increases.