Answer:
Vertex = (1 , 4)
Y-intercept = (0 , 3)
X-intercept = (-1 , 0) and (3 , 0)
Range is y ≤ 4
Axis of symmetry is at x = 1
Step-by-step explanation:
The quadratic function y = ax² + bx + c is represented graphically by a parabola
- The parabola has a vertex point (h , k) which is minimum point if the parabola is opened upward or maximum if it is oped downward
- The axis of symmetry of the parabola is a vertical line passes through the vertex point and its equation is x = h
- The y-intercept is the intersection point between the parabola and the y-xis (value of y at x = 0)
- The x-intercepts are the point of intersection between the parabola and the x-axis (values of x at y = 0)
- The range of the quadratic function is y ≥ k, if the parabola is opened upward or y ≤ k if the parabola is opened downward
From the attached graph
∵ The parabola is opened downward
∵ Its highest point is (1 , 4)
∴ h = 1 and k = 4
∴ Its vertex = (1 , 4)
∵ The parabola intersects the y-axis at point (0 , 3)
∴ The y-intercept = (0 , 3)
∵ The parabola intersects the x-axis at points (-1 , 0) and (3 , 0)
∴ The x-intercept = (-1 , 0) and (3 , 0)
∵ The parabola is opened downward
∴ The range is y ≤ k
∵ k is the value of y of the vertex point
∴ k = 4
∴ The range is y ≤ 4
The axis of symmetry of the parabola is a vertical line passes through the vertex point
∵ The equation of the axis of symmetry is x = h
∵ h is the x-coordinate of the vertex point
∴ h = 1
∴ The axis of symmetry is at x = 1
