Question

The equation of parabola, whose axis is parallel to $y-$axis and which passes through points $(0,2),(-1,0)$ and $(1,6)$ is

• A. $y=x^2+3x+2$
• B. $y=x^2+3x-2$
• C. $x^2+3y+2=0$
• D. $y^2+3x+2=0$

Answer 1

The correct option is A $y=x^2+3x+2$

General equation of such parabola is $y=A{x}^2+Bx+C\cdots \left(1\right)$
Since eqn. $\left(1\right)$ passes through $(0,2),(-1,0)$ and $(1,6),$ then we have
$C=2\cdots \left(2\right)A-B+C=0\cdots \left(3\right)A+B+C=6\cdots \left(4\right)$
From $\left(2\right),\left(3\right)$ and $\left(4\right),$ we get
$A=1,B=3,C=2$
$\therefore$ Equation of parabola is $y=x^2+3x+2$