Answer:
4. (2, 16)
Explanation:
The vertex of a quadratic is where the function changes directions.
Finding the Vertex
As stated the vertex is where the function changed from increasing to decreasing or vice versa. Since this graph opens downward, the vertex will be where the maximum is. The maximum occurs that (2, 16). Therefore, the vertex is also at (2, 16).
Had the quadratic opened upwards, the vertex would occur at the minimum value.
Writing the Equation
Since we know the vertex, we can find the equation for the quadratic. Quadratic formulas can be written as y = a(x - h)² + k. In this formula, a is a constant that tells us whether the graph opens up or down, h is the x-value of the vertex, and k is the y-value of the vertex. So, to find the equation, we can plug in the values we know for the vertex. Then make the a-value negative because we know the graph opens down.