Exploring Vertex Form of Quadratic Functions

What is the general form of a parabola in vertex form?

• y = ax^2 + bx + c

• y = a(x - h)^2 + k

• y = a(x + h)^2 - k

• y = ax^2 + k

How does the value of 'a' affect the direction of a parabola?

• The value of 'a' does not affect the direction.

• Positive 'a' values make the parabola open upwards.

• Negative 'a' values make the parabola open upwards.

• Positive 'a' values make the parabola open downwards.

What does the vertex (h, k) represent in the vertex form of a parabola?

• The intersection point with the y-axis

• The highest or lowest point of the parabola

• The focus of the parabola

• The slope of the parabola

If the vertex form of a parabola is y = 3(x + 2)^2 - 5, what is the vertex?

• (-2, -5)

• (-3, 5)

• (3, 5)

• (2, -5)

What is the axis of symmetry for a parabola with vertex (h, k)?

• y = h

• x = k

• x = h

• y = k

If a parabola's equation is y = -4(x - 3)^2 + 2, in which direction does it open?

• To the right

• To the left

• Upwards

• Downwards

How can you determine the direction a parabola opens from its equation?

• By the sign of 'h' in the equation

• By the sign of 'k' in the equation

• By the sign of 'a' in the equation

• By the degree of the polynomial

In the equation y = a(x - h)^2 + k, what does 'k' represent?

• The x-coordinate of the vertex

• The width of the parabola

• The y-coordinate of the vertex

• The direction of the parabola

Which graph would match a parabola that opens upwards with vertex (1, -2)?

• Graph A

• Graph B

• Graph D

• Graph C

For a parabola facing down, what must be true about the 'a' value?

• It is positive

• It is zero

• It is greater than 1

• It is negative