Question 193761: please show me each step for these three problems along with the solution:
Directions: Write the standard form of the equation of a parabola that contains the given points.
First problem First set of given points (-1,12)(1,0)(2,-3)
Second problem second set of given points (-2,13)(-1,6)(1,4)
Third problem third set of given points (-2,12)(-1,5)(2,20)
Answer by solver91311(24713)   (Show Source):
You can put this solution on YOUR website!
These are all done using the same process.
The general form of the equation of a parabola is:
Substitute the coordinates of your given points into the general equation to obtain 3 linear equations in the three variables A, B, and C. Then solve the system of equations for the values of A, B, and C to obtain the coefficients of your particular quadratic equation.
For your first problem, the first linear equation would be:
The second equation:
And the third:
Solve the system to obtain the values of A, B, and C, and then put these coefficients back into the general form of the equation. Now, depending on what your instructor and/or your text calls the 'standard' form, you are either done, or you must complete the square to put the equation into the vertex form (also referred to as the standard form by some)
(x - h)^2 + k)
John
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