Write the equation of a quadratic function that contains the points (1,21), (2,18), and (-1,9)
1 answer:
Answer:
The equation of a quadratic function that contains the points (1, 21), (2,18) and (-1, 9) is .
Step-by-step explanation:
A quadratic function is a second order polynomial of the form:
(1)
Where:
- Independent variable.
- Dependent variable.
,
,
- Coefficients.
From Algebra we understand that a second order polynomial is determined by knowing three distinct points. If we know that ,
and
, then we construct the following system of linear equations:
(2)
(3)
(4)
By algebraic means, the solution of the system is:
,
,
Therefore, the equation of a quadratic function that contains the points (1, 21), (2,18) and (-1, 9) is .
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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.