Find an equation of the form $y = a x ^ { 2 } + b x + c$ that defines the parabola through the three noncollinear
points given.
-$$( 0 , - 5 ) , ( - 3 , - 2 ) , ( 2,13 )$$
A) $y = - 5 x ^ { 2 } - 2 x + 13$
B) $y = 2 x ^ { 2 } - 3 x$
C) $y = 5 x ^ { 2 } + 2 x - 5$
D) $y = 2 x ^ { 2 } + 5 x - 5$

Question

Quizplus · Accepted Answer

To find the correct equation, we substitute each point into the general form $y = ax^2 + bx + c$ and solve for $a$, $b$, and $c$.1. Using point (0, -5), we get $-5 = a(0)^2 + b(0) + c$, which simplifies to $c = -5$.2. Using point (-3, -2), we get $-2 = a(-3)^2 + b(-3) + c$, which simplifies to $9a - 3b + c = -2$.3. Using point (2, 13), we get $13 = a(2)^2 + b(2) + c$, which simplifies to $4a + 2b + c = 13$.Substituting $c = -5$ into the other two equations and solving the system, we find $a = 2$, $b = 5$, and $c = -5$. Therefore, the correct equation is $y = 2x^2 + 5x - 5$.

Find an Equation of the Form y=ax2+bx+cy = a x ^ { 2 } + b x + cy=ax2+bx+c

Find an Equation of the Form $y = a x ^ { 2 } + b x + c$