Question

opens downward when the downward graph's points are on the left is 0.5,0, on the right is 2.5,0, and on top is 1.5,4, and on the bottom 0, -5. Find the axis of symmetry, does the function have a minimum or maximum. what are the x and y intercepts?

Answer 1

To analyze the parabola defined by the given points, we start by determining its properties. The points specified are:

1. The left point: (0.5, 0)
2. The right point: (2.5, 0)
3. The top vertex point: (1.5, 4)
4. The bottom vertex point: (0, -5)

### 1. Axis of Symmetry
The axis of symmetry for a parabola that opens downward can be found by taking the average of the x-coordinates of the intercepts, which are at (0.5, 0) and (2.5, 0).

\[
\text{Axis of Symmetry} = \frac{x_1 + x_2}{2} = \frac{0.5 + 2.5}{2} = \frac{3}{2} = 1.5
\]

### 2. Maximum or Minimum
Since the parabola opens downward, it has a **maximum** point at the vertex. The vertex provided is at (1.5, 4), which is the highest point of the parabola.

### 3. X-Intercepts
The x-intercepts are where y = 0. According to the provided points, the x-intercepts are:

- (0.5, 0)
- (2.5, 0)

### 4. Y-Intercept
The y-intercept occurs where x = 0. According to the provided point at the bottom:

- The y-intercept is (0, -5).

### Summary
- **Axis of Symmetry:** x = 1.5
- **Maximum or Minimum:** Maximum at (1.5, 4)
- **X-Intercepts:** (0.5, 0) and (2.5, 0)
- **Y-Intercept:** (0, -5)