Find the equation of the parabola of the form $y=a x^{2}+b x+c$ that passes through the given three points.
-$(-2,5),(1,11),(4,35)$
A) $y=x^{2}+3 x+7$
B) $y=x^{2}+2 x+3$
C) $y=x^{2}+2 x+9$
D) $y=x^{2}+4 x+7$

Question

Quizplus · Accepted Answer

To find the correct equation, substitute each point into the general form $y=ax^2+bx+c$ and solve for $a$, $b$, and $c$. For point $(-2,5)$, we get $5=a(-2)^2+b(-2)+c$. For point $(1,11)$, we get $11=a(1)^2+b(1)+c$. For point $(4,35)$, we get $35=a(4)^2+b(4)+c$. Solving these equations simultaneously would give us the values of $a$, $b$, and $c$ that satisfy all three points. By testing the given options, option A, $y=x^2+3x+7$, correctly generates the y-values for all three given points: $(-2,5)$, $(1,11)$, and $(4,35)$.

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

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