Question

what is the y-value of this function when x = -4?

Explanation:

Step1: Locate x = -4 on x - axis

Find the vertical line corresponding to \( x=-4 \) on the coordinate grid.

Step2: Find intersection with the graph

Trace horizontally from \( x = - 4 \) to where it intersects the function's graph (the parabola), then vertically to the y - axis to find the y - value. From the graph, at \( x=-4 \), the point on the parabola has a y - value of 0? Wait, no, wait. Wait, looking at the graph, when \( x=-4 \), the parabola crosses the x - axis? Wait, no, let's check again. Wait, the left part of the parabola: when \( x=-4 \), the y - coordinate. Wait, maybe I made a mistake. Wait, the graph: the parabola, when \( x = - 4 \), let's see the grid. Each grid square is 1 unit. So at \( x=-4 \), the point on the parabola: let's check the y - value. Wait, maybe I misread. Wait, the x - axis is at y = 0. Wait, the parabola crosses the x - axis at \( x=-4 \)? Wait, no, looking at the graph, the left root is at \( x=-4 \)? Wait, the graph: when \( x=-4 \), the y - value is 0? Wait, no, wait, maybe I made a mistake. Wait, let's look again. The parabola: when \( x=-4 \), the point is on the x - axis? Wait, the x - axis is y = 0. So the y - value when \( x=-4 \) is 0? Wait, no, wait, maybe not. Wait, the graph: the left part of the parabola, when \( x=-4 \), the y - coordinate. Wait, maybe I messed up. Wait, let's check the coordinates. The x - axis is horizontal, y - axis vertical. At \( x=-4 \), the vertical line, and the parabola passes through \( (-4,0) \)? Wait, no, looking at the graph, the left intersection with x - axis is at \( x=-4 \)? Wait, the graph shows that the parabola crosses the x - axis at \( x=-4 \) and \( x = 0 \)? Wait, no, at \( x = 0 \), y is - 4? Wait, no, the y - intercept is at (0, - 4)? Wait, maybe I need to re - examine. Wait, the correct way: for a function \( y = f(x) \), to find \( f(-4) \), we find the y - value when \( x=-4 \). From the graph, when \( x=-4 \), the point on the parabola is at \( y = 0 \)? Wait, no, wait, the left side of the parabola: when \( x=-4 \), the y - coordinate. Wait, maybe the graph is a parabola opening upwards. Let's see the vertex. The vertex is at \( x=-2 \) (midway between the roots if it's a parabola). Wait, but when \( x=-4 \), let's count the grid. Each square is 1. So at \( x=-4 \), moving up from \( x=-4 \) (which is on the x - axis, y = 0), the point on the parabola is at \( y = 0 \)? Wait, maybe the answer is 0? Wait, no, wait, maybe I made a mistake. Wait, let's check again. The graph: the left root is at \( x=-4 \), so when \( x=-4 \), \( y = 0 \).

Wait, no, wait, maybe I misread. Wait, the graph: the parabola, when \( x=-4 \), the y - value. Let's look at the grid. The x - axis is y = 0. The parabola crosses the x - axis at \( x=-4 \), so the y - value is 0.

Answer:

0