Question

Find the approximate zeros of h(x) = -2 – 2x + 6graphically.

Answer 1

We have an equation that represents a line. We can rewrite the equation as follows:

`h(x)=-2-2x+6\rightarrow h(x)=-2x+4`

For finding two points of the equation in order to find the line, we can proceed as follows:

• First, the line has a slope m = -2 (it is negative), so as the values for x increments, the values for y has a negative increment (or the values are less as the values tends to infinity)

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• Second, give two values for the line, for example, when x = -5 and when x = 5.

In this case, for x = -5:

`y=-2x+4\rightarrow y=-2\cdot(-5)+4\rightarrow y=10+4\rightarrow y=14`

For x = 5

`y=-2\cdot(5)+4\rightarrow-10+4\rightarrow y=-6`

Then we have to points of the line (-5, 14) and (5, -6). Then, the graph representation is (approximately):

Graphically, the zero for the expression is near to 2.

For y = 0, we have that

`y=-2x+4\rightarrow0=-2x+4\rightarrow2x=4\rightarrow x=2`

So, the zero for this line is 2. Therefore, graphically, we approximate the zero to a value near to 2. The actual value is 2. We can make this for any other type of graph. As more precise the graph, the more accurate will be the result graphically.