Understanding Quadratic Functions and Their Properties

What is the standard form of a quadratic function?

• f(x) = ax^2 + bx + c

• f(x) = a(x - h)^2 + k

• f(x) = ax + b

• f(x) = a(x + h)^2 - k

If 'a' is negative in the standard form of a quadratic function, what is the direction of the parabola?

• It opens upwards

• It opens downwards

• It opens to the right

• It opens to the left

How does increasing the value of 'a' affect the graph of a quadratic function?

• The parabola shifts to the right

• The parabola shifts to the left

• The parabola becomes narrower

• The parabola becomes wider

What happens to the parabola when the value of 'h' is increased?

• It shifts to the left

• It shifts to the right

• It shifts downwards

• It shifts upwards

In the example, what is the vertex of the quadratic function y = (x - 3)^2 - 4?

• (-3, 4)

• (3, -4)

• (-3, -4)

• (3, 4)

What is the equation of the axis of symmetry for the function y = (x - 3)^2 - 4?

• y = 3

• x = -3

• x = 3

• y = -3

How do you find the y-intercept of a quadratic function in standard form?

• Set both x and y to zero

• Set y to zero and solve for x

• Set x to zero and solve for y

• Set the vertex to zero

In the second example, what is the y-intercept of the function y = -2(x + 1)^2 + 8?

• (0, -6)

• (0, -8)

• (0, 6)

• (0, 8)

What is the x-intercept of the function y = -2(x + 1)^2 + 8 when solved?

• (0, 1) and (0, -1)

• (1, 0) and (-3, 0)

• (3, 0) and (-1, 0)

• (2, 0) and (-2, 0)

What is the significance of the axis of symmetry in a parabola?

• It is the line that divides the parabola into two symmetrical halves

• It indicates the maximum point of the parabola

• It shows the direction in which the parabola opens

• It determines the width of the parabola