We want to use the given graph to determine the zeroes of the given quadratic function. The zeroes are the x-coordinates of the points of intersection of the parabola and the x-axis. Recall that a quadratic function can have two, one, or no zeroes.
Let's consider the graph.
We can see that the parabola intersects the x-axis twice. The first point of intersection seems to be between x=-1 and x=0, and the second one, between x=2 and x=3. To approximate the zeroes, we will make tables using x-values using an increment of 0.1. Let's start with the table for x between -1 and 0.
x
-0.9
-0.8
-0.7
-0.6
-0.5
-0.4
-0.3
-0.2
-0.1
f(x)
-1.61
-1.24
-0.89
-0.56
-0.25
0.04
0.31
0.56
0.79
As we can see, the change in signs happens between x=-0.5 and x=-0.4, and the function value is closer to 0 for x=-0.4. Therefore, the first point of intersection is about x=-0.4. Let's make another table, this time for x between 2 and 3.
x
2.1
2.2
2.3
2.4
2.5
2.6
2.7
2.8
2.9
f(x)
0.79
0.56
0.31
0.04
-0.25
-0.56
-0.89
-1.24
-1.61
This time the change in signs happens between x=2.4 and x=2.5, and the function value is closer to 0 for x=2.4. Therefore, the second point of intersection is about x=2.4, so the zeroes of f are about -0.4 and 2.4.
Mathleaks uses cookies for an enhanced user experience. By using our website, you agree to the usage of cookies as described in our policy for cookies.
