Question

example 4 identify the intercepts and extreme points. write your answer as ordered pairs. if none exist, write none. x - intercept(s) y - intercept(s) maximum point(s) minimum point(s)

Explanation:

Step1: Define x - intercept

The x - intercepts are the points where the graph crosses the x - axis (y = 0).

Step2: Observe the graph

From the graph, the curve crosses the x - axis at two points. Let's assume the x - values of these points are \(x_1\) and \(x_2\). If we estimate from the graph, the x - intercepts are \((x_1,0)\) and \((x_2,0)\).

Step3: Define y - intercept

The y - intercept is the point where the graph crosses the y - axis (x = 0).

Step4: Locate on the graph

The graph crosses the y - axis at a single point \((0,y_0)\).

Step5: Define maximum point

The maximum point of a parabola opening downwards is the vertex.

Step6: Identify from graph

The vertex of the parabola (the highest point) is \((x_{v},y_{v})\).

Step7: Define minimum point

Since this is a parabola opening downwards, there is no minimum point.

Answer:

x - intercept(s): (Two points where the graph crosses x - axis, e.g., \((- 2,0)\) and \((2,0)\) depending on actual graph)
y - intercept(s): (Point where the graph crosses y - axis, e.g., \((0,2)\) depending on actual graph)
Maximum point(s): (Vertex of the parabola, e.g., \((0,4)\) depending on actual graph)
Minimum point(s): none