Write the equation of the quadratic function whose graph is a parabola containing the given points.
-$( 0,3 ) , ( 3,15 ) , ( - 3,27 )$
A) $y = 2 x ^ { 2 } + 2 x + 1$
B) $y = 3 x ^ { 2 } - 2 x + 3$
C) $y = 2 x ^ { 2 } - 2 x + 3$
D) $y = 2 x ^ { 2 } - x + 3$

Question

Quizplus · Accepted Answer

To find the correct equation, substitute the given points into the general form of a quadratic equation $y = ax^2 + bx + c$ and solve for $a$, $b$, and $c$. Using the point (0,3), we get $c = 3$. Substituting the points (3,15) and (-3,27) into the equation and solving the system of equations will show that $a = 2$ and $b = -2$, leading to the equation $y = 2x^2 - 2x + 3$.

Write the Equation of the Quadratic Function Whose Graph Is (0,3),(3,15),(−3,27)( 0,3 ) , ( 3,15 ) , ( - 3,27 )(0,3),(3,15),(−3,27)

Write the Equation of the Quadratic Function Whose Graph Is $( 0,3 ) , ( 3,15 ) , ( - 3,27 )$