Write the equation of the quadratic function whose graph is a parabola containing the given points.
-$( 0,5 ) , ( - 1,5.25 ) , ( 5,18.75 )$
A) $y = \frac { x ^ { 2 } } { 2 } + \frac { x } { 4 } - 5$
B) $y = \frac { x ^ { 2 } } { 2 } + 2 x + 5$
C) $y = \frac { x ^ { 2 } } { 2 } + \frac { x } { 4 } + 5$
D) $y = \frac { x ^ { 2 } } { 4 } + \frac { x } { 2 }$

Question

Quizplus · Accepted Answer

The general form of a quadratic equation is $y = ax^2 + bx + c$. By substituting the given points into this equation, we can form a system of equations to solve for $a$, $b$, and $c$. Using the point $(0,5)$, we immediately find $c = 5$. Substituting the points $(-1,5.25)$ and $(5,18.75)$ into the equation and solving the system, we find $a = \frac{1}{2}$ and $b = \frac{1}{4}$, leading to the equation $y = \frac{x^2}{2} + \frac{x}{4} + 5$, which matches choice C.

Write the Equation of the Quadratic Function Whose Graph Is (0,5),(−1,5.25),(5,18.75)( 0,5 ) , ( - 1,5.25 ) , ( 5,18.75 )(0,5),(−1,5.25),(5,18.75)

Write the Equation of the Quadratic Function Whose Graph Is $( 0,5 ) , ( - 1,5.25 ) , ( 5,18.75 )$