Question

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

Answer 1

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 \( k = 2 \).

2. **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.

3. **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!