To identify the key features of the parabola, let’s start with the information provided:
- 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 \( k = 2 \).
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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.
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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!