Write the equation of the quadratic function whose graph is a parabola containing the given points.
-$( 0 , - 1 ) , ( 4,51 ) , ( - 2,9 )$
A) $y = 3 x ^ { 2 } + x - 1$
B) $y = 3 x ^ { 2 } - x - 1$
C) $y = 2 x ^ { 2 } + x - 1$
D) $y = 3 x ^ { 2 } + x - 2$

Question

Quizplus · Accepted Answer

The general form of a quadratic equation is $y = ax^2 + bx + c$. Substituting each given point into this equation gives a system of equations that can be solved for $a$, $b$, and $c$. For the point $(0, -1)$, the equation is $-1 = a(0)^2 + b(0) + c$, which simplifies to $c = -1$. For the point $(4, 51)$, the equation is $51 = a(4)^2 + b(4) + c$, which simplifies to $51 = 16a + 4b - 1$ when substituting $c = -1$. For the point $(-2, 9)$, the equation is $9 = a(-2)^2 + b(-2) + c$, which simplifies to $9 = 4a - 2b - 1$ when substituting $c = -1$. Solving this system of equations yields $a = 3$, $b = 1$, and $c = -1$, which corresponds to the equation $y = 3x^2 + x - 1$.

Write the Equation of the Quadratic Function Whose Graph Is (0,−1),(4,51),(−2,9)( 0 , - 1 ) , ( 4,51 ) , ( - 2,9 )(0,−1),(4,51),(−2,9)

Write the Equation of the Quadratic Function Whose Graph Is $( 0 , - 1 ) , ( 4,51 ) , ( - 2,9 )$