Understanding Quadratic Functions

What is the condition for a function to be classified as a quadratic function?

• The highest exponent of x is 1.

• The highest exponent of x is 2.

• The function includes a logarithm.

• The function is linear.

How does the value of 'a' affect the direction in which a parabola opens?

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

• If 'a' is positive, the parabola opens up.

• If 'a' is negative, the parabola opens up.

• If 'a' is positive, the parabola opens down.

What is the vertex of a parabola that opens down?

• The intersection with the y-axis.

• The lowest point on the graph.

• The highest point on the graph.

• The midpoint of the graph.

What is the axis of symmetry in a parabola?

• A horizontal line through the vertex.

• A vertical line through the vertex.

• A diagonal line through the vertex.

• A line that does not pass through the vertex.

In the standard form of a quadratic function, what does the 'h' in x-h represent?

• The vertical shift of the parabola.

• The y-intercept of the parabola.

• The horizontal shift of the parabola.

• The slope of the parabola.

How can you determine the axis of symmetry from the standard form of a quadratic function?

• It is always y = k.

• It is always x = h.

• It is always y = h.

• It is always x = k.

What is the vertex of the function f(x) = -2(x-5)^2 - 1?

• (-5, 1)

• (5, -1)

• (-5, -1)

• (5, 1)

For the function g(x) = (x+2)^2 + 3, what is the axis of symmetry?

• x = 3

• x = -2

• x = -3

• x = 2

What happens to the graph of f(x) = x^2 when it is transformed to g(x) = (x-3)^2 + 2?

• It shifts 3 units right and 2 units down.

• It shifts 3 units right and 2 units up.

• It shifts 3 units left and 2 units down.

• It shifts 3 units left and 2 units up.

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

• The x-intercept of the parabola.

• The slope of the parabola.

• The vertical shift of the parabola.

• The horizontal shift of the parabola.