FX parabola

Determine the equation of the parabola going through the following co-ordinates (1;2), (-1;-2), and (2;7)

Correct answer:

y = x^2+2x-1

Step-by-step explanation:

A=(1,2) B=(−1,−2) C=(2,7)  y=f(x)=a⋅ x2+b⋅ x+c  Ay​=a⋅ Ax2​+b⋅ Ax​+c By​=a⋅ Bx2​+b⋅ Bx​+c Cy​=a⋅ Cx2​+b⋅ Cx​+c 2=a⋅ 12+b⋅ 1+c (−2)=a⋅ (−1)2+b⋅ (−1)+c 7=a⋅ 22+b⋅ 2+c  a+b+c=2 a−b+c=−2 4a+2b+c=7  Pivot:Row1↔Row3 4a+2b+c=7 a−b+c=−2 a+b+c=2  Row2−41​⋅ Row1→Row2 4a+2b+c=7 −1.5b+0.75c=−3.75 a+b+c=2  Row3−41​⋅ Row1→Row3 4a+2b+c=7 −1.5b+0.75c=−3.75 0.5b+0.75c=0.25  Row3−−1.50.5​⋅ Row2→Row3 4a+2b+c=7 −1.5b+0.75c=−3.75 c=−1  c=1−1​=−1 b=−1.5−3.75−0.75c​=−1.5−3.75−0.75⋅ (−1)​=2 a=47−2b−c​=47−2⋅ 2+1​=1  a=1 b=2 c=−1  y=x2+2x−1

Try another example


Did you find an error or inaccuracy? Feel free to write us. Thank you!







Tips for related online calculators
Are you looking for help with calculating roots of a quadratic equation?
Do you have a linear equation or system of equations and looking for its solution? Or do you have a quadratic equation?

You need to know the following knowledge to solve this word math problem:

Grade of the word problem:


 
We encourage you to watch this tutorial video on this math problem: video1

Related math problems and questions: