Answer:
The y-intercept is (0, 8)
The x-intercepts are (2, 0) and (4, 0)
The axis of symmetry is a vertical line at x = 3
The vertex is (3, -1)
The graph has a minimum value -1 at x = 3
The domain is {x: x ∈ R} ⇒ (-∞, ∞)
The range is {y: y ≥ -1} ⇒ [-1, ∞)
Step-by-step explanation:
By using the given figure
The figure represents a parabola (the graph of a quadratic function
∵ The parabola intersects the y-axis at point (0, 8)
∴ The y-intercept is (0, 8)
∵ The parabola intersects the x-axis at point (2, 0) and (4, 0)
∴ The x-intercepts are (2, 0) and (4, 0)
∵ The axis of symmetry of the parabola is a vertical line that passes
through the vertex of it
∵ The x-coordinate of the vertex point is 3
∴ The axis of symmetry is a vertical line at x = 3
∵ The vertex of the parabola is the lowest point on the graph
∵ The lowest point is (3, -1)
∴ The vertex is (3, -1)
∵ The vertex point of the graph is the lowest
∴ The graph has a minimum value -1 at x = 3
∵ The domain is all values of x belong to the parabola
∵ x could be any real number
∴ The domain is {x: x ∈ R} ⇒ (-∞, ∞)
∵ The range is all the values of y from the lowest point
∵ The y-coordinate of the lowest point is -1
∴ The range is {y: y ≥ -1} ⇒ [-1, ∞)
