Question

Describe the intervals of increasing/decreasing of the following quadratic function graphed. (4 points) The quadratic function is Increasing from to and decreasing from to
0
1
2
3
4
positive infinity
negative infinity

Answer 1

To determine the intervals of increasing and decreasing for a quadratic function, we first need to identify the vertex and the direction of the parabola (whether it opens upwards or downwards).

For a quadratic function in the standard form \(f(x) = ax^2 + bx + c\):

- If \(a > 0\), the parabola opens upwards, and the vertex is the minimum point.
- If \(a < 0\), the parabola opens downwards, and the vertex is the maximum point.

The function will be:

1. **Decreasing** on the interval from negative infinity to the x-coordinate of the vertex.
2. **Increasing** on the interval from the x-coordinate of the vertex to positive infinity.

Assuming the vertex \(x\) coordinate is at \(x = h\), where \(h = -\frac{b}{2a}\):

- The function is **decreasing** from \(-\infty\) to \(h\).
- The function is **increasing** from \(h\) to \(+\infty\).

To fill in the blanks based on this understanding:

- The quadratic function is increasing from \(h\) to \(+\infty\) (where \(h\) is the x-coordinate of the vertex).
- The quadratic function is decreasing from \(-\infty\) to \(h\).

Without the specific coefficients of the quadratic function, I can't provide the exact numerical values for \(h\). However, apply the formula \( h = -\frac{b}{2a} \) using your function’s coefficients to find the specific intervals.