Using the given graph of the
equation 𝑦 equals 𝑥 squared plus two 𝑥 minus five, find which of the following is
the best approximation for the solutions to 𝑥 squared plus two 𝑥 minus five equals
zero. The answers are A) 𝑥 is equal to
negative three or one. B) 𝑥 is equal to negative 3.5 or
1.5. Or C) 𝑥 is equal to negative four
Well, to solve this problem, we
want to see where our graph has a 𝑦-value equal to zero. And that’s because we want to find
solutions to 𝑥 squared plus two 𝑥 minus five is equal to zero. And if we take a look at our graph,
we’re gonna see that there’re two points where this occurs.
Now to find the 𝑥-values of these
two points, so the solution to approximation for the solutions, we need to be able
to read off what values they are. And to do that, we need to know
what is the scale of our graph. We can see the scale is one square
is equal to 0.5. So therefore, we can see that the
two values we can get from our graph are going to be negative 3.5 and 1.5.
So therefore, the best
approximation for the solutions to 𝑥 squared plus two 𝑥 minus five equals zero is
going to be B. And that’s 𝑥 equals negative 3.5
or 1.5. And this is the case because these
are the two points where our graph crosses the 𝑥-axis, so therefore where 𝑦 would
be equal to zero.
And if we take a look at the other
two options, we could see that C would be too great. So the values are actually bigger
than the values that we would get if we crossed the 𝑥-axis on our graph. And A would give us values that are
too small because you could see that these are less than the values that we get if
we found the point where the graph crosses the 𝑥-axis.