Solve the problem.
-Find the equation of the parabola $y = a x ^ { 2 } + b x + c$ that passes through the points $( - 2,0 ) , ( 0 , - 4 )$, and $( 3,3 )$.
A) $y = - \frac { 7 } { 15 } x ^ { 2 } - \frac { 4 } { 15 } x - 7$
B) $y = \frac { 1 } { 5 } x ^ { 2 } - \frac { 8 } { 15 } x - \frac { 4 } { 3 }$
C) $y = \frac { 13 } { 15 } x ^ { 2 } - \frac { 4 } { 15 } x - 4$
D) $y = - \frac { 4 } { 15 } x ^ { 2 } + \frac { 13 } { 15 } x - 4$

Question

Quizplus · Accepted Answer

By substituting the given points into the general form of the parabola equation, we can set up a system of equations to solve for $a$, $b$, and $c$. Solving this system gives the equation $y = \frac { 13 } { 15 } x ^ { 2 } - \frac { 4 } { 15 } x - 4$.

Solve the Problem y=ax2+bx+cy = a x ^ { 2 } + b x + cy=ax2+bx+c

Solve the Problem $y = a x ^ { 2 } + b x + c$