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)