Find an equation of the form $y = a x ^ { 2 } + b x + c$ whose graph passes through the points $( 1,7 ),$ $( - 4 , - 18 ),$ and $( - 1,3 ).$
A) $y = - x ^ { 2 } + 2 x + 6$
B) $y = - x ^ { 2 } + 6 x + 2$
C) $y = 2 x ^ { 2 } - x + 6$
D) $y = 6 x ^ { 2 } - x + 2$
E) $y = 6 x ^ { 2 } + 2 x - 1$

Question

Quizplus · Accepted Answer

To find the correct equation, substitute the x and y values from each point into the general form $y = ax^2 + bx + c$ and solve the system of equations. For point (1,7), we get $7 = a(1)^2 + b(1) + c$. For point (-4, -18), we get $-18 = a(-4)^2 + b(-4) + c$. For point (-1, 3), we get $3 = a(-1)^2 + b(-1) + c$. Solving this system, we find that $a = -1$, $b = 2$, and $c = 6$, which matches option A: $y = -x^2 + 2x + 6$.

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