Identify these key features of the parabola. (2 points) vertex: (4,2) (smaller) x-intercept: () (larger) x-intercept: () y-intercept: ()

1 answer

To identify the key features of the parabola, let’s start with the information provided:

  1. Vertex: (4, 2)

This indicates that the parabola is likely in vertex form, which can be expressed as: \[ y = a(x - h)^2 + k \] where \( (h, k) \) is the vertex. In this case, \( h = 4 \) and \( k = 2 \).

  1. X-Intercepts: To determine the x-intercepts, you would typically set \( y = 0 \) and solve for \( x \). The specific values of x-intercepts depend on the value of \( a \) in the equation, which is not given here.

  2. Y-Intercept: The y-intercept can be found by putting \( x = 0 \) in the vertex form equation. Thus, you would calculate: \[ y = a(0 - 4)^2 + 2 = 16a + 2 \] The y-intercept depends on the value of \( a \).

Summary of Key Features

Without the specific values for \( a \), the x-intercepts cannot be determined, but we can outline the relationships for finding them:

  • Vertex: (4, 2)
  • X-Intercepts: To find the x-intercepts, you would need to know \( a \) (which determines the specific intercepts).
  • Y-Intercept: \( (0, 16a + 2) \)

To complete the specific points for the x-intercepts and y-intercept, more information about the parabola (specifically the direction and width/a value) is needed. If you have an equation or a specific parabola in mind, please provide it!