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

Answer 1

To determine the intervals of increasing and decreasing for a quadratic function, we can analyze the function in vertex form or standard form. The general form of a quadratic function is:

\[ f(x) = ax^2 + bx + c \]

where \( a \) determines the direction of the parabola (opening upwards if \( a > 0 \) and downwards if \( a < 0 \)).

### Step 1: Find the Vertex
The vertex of the quadratic function can be determined using the vertex formula:

\[ x = -\frac{b}{2a} \]

This x-value of the vertex is where the function changes from increasing to decreasing (or vice versa).

### Step 2: Determine Intervals
- If the parabola opens upwards (\( a > 0 \)), the function will be:
- **Decreasing** on the interval \((- \infty, -\frac{b}{2a})\)
- **Increasing** on the interval \((- \frac{b}{2a}, \infty)\)

- If the parabola opens downwards (\( a < 0 \)), the function will be:
- **Increasing** on the interval \((- \infty, -\frac{b}{2a})\)
- **Decreasing** on the interval \((- \frac{b}{2a}, \infty)\)

### Example
Assuming you have a specific quadratic function, you can plug in the values of \( a \) and \( b \) to find the intervals.

### Conclusion
To provide specific intervals, please provide the coefficients \( a \) and \( b \) for the quadratic function you are analyzing. Then, intervals of increasing/decreasing can be specified accurately.