Question

use the image to answer the question.
identify these key features of the parabola.
remember that each of these features must be written as an ordered pair.
(2 points)
vertex:
(smaller) x - intercept:
(larger) x - intercept:
y - intercept:

Explanation:

Step1: Find the vertex

The vertex of a parabola is the highest or lowest point. For this downward - opening parabola, it's the peak. From the graph, the vertex is at \(x = 4\) and \(y=2\), so the vertex is \((4,2)\).

Step2: Find the x - intercepts

The x - intercepts are the points where the parabola crosses the x - axis (\(y = 0\)). From the graph, the parabola crosses the x - axis at \(x = 2\) and \(x = 6\). The smaller x - intercept is \((2,0)\) and the larger x - intercept is \((6,0)\).

Step3: Find the y - intercept

The y - intercept is the point where the parabola crosses the y - axis (\(x = 0\)). From the graph, when \(x = 0\), \(y=-6\), so the y - intercept is \((0, - 6)\).

Answer:

vertex: \((4,2)\)
(smaller) x - intercept: \((2,0)\)
(larger) x - intercept: \((6,0)\)
y - intercept: \((0,-6)\)