Question

use the graph to estimate the x- and y-intercepts of the function and describe where the function is positive and negative.
x-intercept(s): select choice
y-intercept: select choice
positive: when select choice
negative: when select choice

Explanation:

Step1: Identify x - intercepts

The x - intercepts are the points where the graph intersects the x - axis (where \(y = 0\)). From the graph (a parabola opening upwards), we can see that the graph intersects the x - axis at \(x=-2\) and \(x = 2\) (assuming the grid has integer coordinates, and the distance from the origin to the intersection points is 2 units). So the x - intercepts are \((-2,0)\) and \((2,0)\) or \(x=-2\) and \(x = 2\).

Step2: Identify y - intercept

The y - intercept is the point where the graph intersects the y - axis (where \(x = 0\)). From the graph, the vertex of the parabola (the lowest point) is at \((0,-4)\)? Wait, no, looking at the graph, when \(x = 0\), the y - coordinate of the point on the graph is \(-4\)? Wait, no, maybe I misread. Wait, the parabola is opening upwards, and the vertex is on the y - axis. Let's check the grid. If the vertex is at \((0, - 4)\)? No, maybe the y - intercept is at \((0,-4)\)? Wait, no, let's think again. Wait, the x - intercepts: let's assume the grid has each square as 1 unit. The graph crosses the x - axis at \(x=-2\) and \(x = 2\) (so x - intercepts are \(-2\) and \(2\)). The y - intercept is the point where \(x = 0\), so looking at the graph, when \(x = 0\), the y - value is \(-4\)? Wait, no, maybe the vertex is at \((0,-4)\), so the y - intercept is \((0,-4)\)? Wait, no, the y - intercept is the value of \(y\) when \(x = 0\), so from the graph, the point on the y - axis is \((0,-4)\)? Wait, maybe I made a mistake. Wait, the graph is a parabola opening upwards, symmetric about the y - axis. Let's see the x - intercepts: when \(y = 0\), \(x=-2\) and \(x = 2\). When \(x = 0\), \(y=-4\) (so y - intercept is \(-4\)).

Step3: Determine where the function is positive

A function is positive when its graph is above the x - axis (\(y>0\)). For a parabola opening upwards with x - intercepts at \(x=-2\) and \(x = 2\), the graph is above the x - axis when \(x<-2\) or \(x>2\) (because outside the roots, the parabola is above the x - axis).

Step4: Determine where the function is negative

A function is negative when its graph is below the x - axis (\(y < 0\)). For the parabola, between the x - intercepts (\(-2

Answer:

x - intercept(s): \(-2\) and \(2\) (or \((-2,0)\) and \((2,0)\))
y - intercept: \(-4\) (or \((0,-4)\))
positive: when \(x < - 2\) or \(x>2\)
negative: when \(-2

(Note: The actual values may depend on the exact grid. If the grid has each square as 1 unit, and the x - intercepts are at \(x=-2\) and \(x = 2\), y - intercept at \(y=-4\), positive for \(x < - 2\) or \(x>2\), negative for \(-2