The sum of the squares of two consecutive negative integers is 61. Find the smaller of the two integers
1 answer:
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Answer:
the parabola can be written as:
f(x) = y = a*x^2 + b*x + c
first step.
find the vertex at:
x = -b/2a
the vertex will be the point (-b/2a, f(-b/2a))
now, if a is positive, then the arms of the parabola go up, if a is negative, the arms of the parabola go down.
The next step is to see if we have real roots by using the Bhaskara's equation:
Now, draw the vertex, after that draw the values of the roots in the x-axis, and now conect the points with the general draw of the parabola.
If you do not have any real roots, you can feed into the parabola some different values of x around the vertex
for example at:
x = (-b/2a) + 1 and x = (-b/2a) - 1
those two values should give the same value of y, and now you can connect the vertex with those two points.
If you want a more exact drawing, you can add more points (like x = (-b/2a) + 3 and x = (-b/2a) - 3) and connect them, as more points you add, the best sketch you will have.
Given:
x is a number between 8 and 12 exclusive.
To find:
The value of x.
Solution:
It is given that x is a number between 8 and 12 exclusive. It means the value of x lies between 8 and 12 but 8 and 12 are not included.
The whole numbers for range are 9, 10, 11.
Therefore, the values of x are 9, 10, 11 and the value of x in the form of inequality is .