When a parabola opens “down” the vertex is known as a
The correct answer and explanation is:
When a parabola opens “down,” the vertex is known as the maximum point. This is because the vertex represents the highest point on the graph of the parabola, given that it opens downwards. In other words, the vertex is the point at which the parabola reaches its greatest y-value.
A standard parabola is expressed by the equation y=ax2+bx+cy = ax^2 + bx + c, where aa, bb, and cc are constants. The direction in which the parabola opens depends on the value of the coefficient aa. If a>0a > 0, the parabola opens upwards, and if a<0a < 0, the parabola opens downwards.
For a parabola that opens down, the vertex is located at the point where the axis of symmetry intersects the parabola. This axis of symmetry is a vertical line passing through the vertex, and it divides the parabola into two mirror-image halves. The vertex has the x-coordinate x=−b2ax = \frac{-b}{2a}, which is derived from the general form of the quadratic equation. Once this x-coordinate is found, it can be substituted back into the equation to find the y-coordinate of the vertex.
The maximum value of the quadratic function occurs at the vertex when the parabola opens down. This maximum y-value represents the highest point that the parabola reaches, and from there, the parabola descends as you move away from the vertex in either direction along the x-axis. This feature is crucial in various real-world applications, such as projectile motion, where the vertex represents the peak of the object’s trajectory before it begins to descend.