Question

Use a system of equations to find the specified equation that passes through the points. Solve the system using matrices. Show your work. Parabola: y = ax2 + bx + c
(GRAPH BELOW) HELPPPP!

Answer 1

Start by plugging in the points to get the 3 equations in terms of a,b,c. Then you have:
\[\vec{v}=(a,b,c)^T \implies A \vec{v}=\vec{b}\]
Where b is is the vector coming from the equations. From there if the determinant of A is nonzero you can invert A and multiply both sides ON THE LEFT by A giving:
\[A^{-1}A\vec{v}=I\vec{v}=A^{-1} \vec{b}\]
Doing the simple matrix multiplication yields your solutions for a,b, and c. Plugging that in you find your equation for your parabola.