Question

Which of the following equations can represent a parabola whose axis of symmetry is the line $x=-3$ and has minimum value of $5$?

• A. $y=(x-3{)}^2+5$
• B. $y=(x+3{)}^2+5$
• C. $y=(x-5{)}^2+3$
• D. $y=(x+5{)}^2-3$

Answer 1

Answer: (B)

$y=(x+3{)}^2+5$

Let the equation of the parabola be of the type $y-\beta =(x-\alpha {)}^2$. Now $(x-\alpha {)}^2\ge 0$.

Hence $(y-\beta )\ge 0$ or $y\ge \beta$.

Thus minimum value will be $y=\beta$.

Now it is given that the minimum value is $5$.

Hence, $\beta =5$

It is also given that the parabola is symmetric about $x=-3$.

Hence $\alpha =-3$

Thus the equation becomes $(x+3{)}^2=y-5$. $y=(x+3{)}^2+5$.