Answer:
The x intercepts are b , - b
The y-intercept is - b²
The vertex is (0 , - b²)
The axis of symmetry of the function is the y-axis
Explanation:
* Lets explain the key aspects of the quadratic function
- There are many key aspects in a quadratic graph such as:
# x-intercepts
# y-intercept
# The vertex
# Axis of symmetry
* Lets solve the problem
∵ f(x) = x² - b² is a quadratic function
∵ The general form of the quadratic function is f(x) = Ax² + B(x) + C
where A , B , C are constant
∴ A = 1 , B = 0 , C = -b²
- To find the x-intercept put f(x) = 0
∵ f(x) = x² - b²
∴ x² - b² = 0 ⇒ add b² for both sides
∴ x² = b² ⇒ take √ for both sides
∴ x = ± b
∴ The x intercepts are b , - b
- To find the y-intercept put x = 0
∵ f(x) = x² - b²
∴ f(0) = 0 - b²
∴ f(0) = - b²
∴ The y-intercept is - b²
- The vertex of the function is (h , k) where h = -B/2A and k = f(h)
∵ A = 1 and B = 0
∴ h = 0/2(1) = 0
∵ k = f(h)
∴ k = f(0) = 0 - b² = - b²
∴ k = - b²
∴ The vertex is (0 , - b²)
- The axis of symmetry of the quadratic function is a vertical line
passes through the vertex of it and its equation is x = h
∵ h = 0
∴ The equation of the axis of symmetry is x = 0
∵ The equation of the y-axis is x = 0
∴ The axis of symmetry of the function is the y-axis