Question

Vertex= Y-intercept= X-intercept= Range= Axis of symmetry =

Answer 1

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