Explore the Quadratic Vertex: Does y = -x² + 3x + 9 Have a Maximum or Minimum?

Does the parable

$y=-x^2+3x+9$

Is there a minimum or maximum point?

The quadratic function is given by $y = -x^2 + 3x + 9$.

In the general quadratic form $y = ax^2 + bx + c$, the coefficient $a$ determines the parabola's orientation:

• If $a > 0$: The parabola opens upwards, indicating a minimum point.
• If $a < 0$: The parabola opens downwards, indicating a maximum point.

For this function, $a = -1$. Since $a < 0$, the parabola opens downwards.

Therefore, the function has a maximum point.

Thus, the correct answer is the function has a highest point.

Therefore, the solution to the problem is choice 2: Highest point.