Question

describe the key characteristics of the given parabola. vertex: axis of symmetry: zeros: and does the graph show a maximum or minimum? maximum/minimum value: range:

Explanation:

Step1: Locate vertex

The vertex is the lowest point of the parabola. By observing the graph, the vertex is at the point where the parabola changes direction. Let's assume the grid - lines are in unit intervals. The vertex is at $(2, - 4)$.

Step2: Determine axis of symmetry

The axis of symmetry is a vertical line passing through the vertex. For a parabola, its equation is $x =$ the $x$ - coordinate of the vertex. So the axis of symmetry is $x = 2$.

Step3: Find zeros

The zeros are the $x$ - values where the parabola intersects the $x$ - axis. By looking at the graph, the parabola intersects the $x$ - axis at $x = 0$ and $x = 4$.

Step4: Identify max/min

Since the parabola opens upwards (the U - shape is upward), it has a minimum.

Step5: Find min value

The minimum value is the $y$ - coordinate of the vertex, which is $y=-4$.

Step6: Determine range

The range is the set of all possible $y$ - values. Since the minimum $y$ - value is $-4$ and the parabola opens upwards, the range is $y\geq - 4$.

Answer:

Vertex: $(2, - 4)$
Axis of Symmetry: $x = 2$
Zeros: $0$ and $4$
Does the graph show a maximum or minimum?: Minimum
Maximum/minimum value: $-4$
Range: $y\geq - 4$