2 Multiple Choice 20 points
Which function has a maximum?

Ask by Griffin Vaughn. in the United States

Jan 29,2025

Question

2 Multiple Choice 20 points Which function has a maximum? $$ y=-3(x+9)^{2}-1 $$ $$ y=\frac{1}{8}(x-4)^{2}+10 $$ $$ y=8+(x-4)^{2} $$ $$ y=16 x^{2}+9 $$

UpStudy AI · Accepted Answer

The function that has a maximum is the one where the parabola opens downward. This occurs when the coefficient $$ a $$ in the quadratic function $$ y = a(x-h)^2 + k $$ is negative.

Let's analyze each option:

1. **$$ y = -3(x+9)^2 -1 $$**
   - Here, $$ a = -3 $$ (which is negative).
   - The parabola opens downward, indicating a **maximum** value.

2. **$$ y = \frac{1}{8}(x-4)^2 +10 $$**
   - Here, $$ a = \frac{1}{8} $$ (which is positive).
   - The parabola opens upward, indicating a **minimum** value.

3. **$$ y = 8 + (x-4)^2 $$**
   - This can be rewritten as $$ y = 1(x-4)^2 + 8 $$, where $$ a = 1 $$ (positive).
   - The parabola opens upward, indicating a **minimum** value.

4. **$$ y = 16x^2 +9 $$**
   - Here, $$ a = 16 $$ (positive).
   - The parabola opens upward, indicating a **minimum** value.

**Conclusion:** Only the first function $$ y = -3(x+9)^2 -1 $$ has a maximum.

**Answer:** $$ y=-3(x+9)^{2}-1 $$
The function $$ y = -3(x+9)^2 -1 $$ has a maximum.

2 Multiple Choice 20 points
Which function has a maximum?

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