Question

Which of the following equations is of a parabola with a vertex at (0, 3)? y = (x - 3) 2 y = (x + 3) 2 y = x 2 - 3 y = x 2 + 3

Answer 1

SOLUTION

TO CHOOSE THE CORRECT OPTION

Which of the following equations is of a parabola with a vertex at (0, 3)

$\sf{1. \: \: y = {(x - 3)}^{2} }$

$\sf{2. \: \:y = {(x + 3)}^{2} }$

$\sf{3. \: \: y = {x}^{2} - 3}$

$\sf{4. \: \: y = {x}^{2} + 3}$

CONCEPT TO BE IMPLEMENTED

The equation of a parabola with vertex at (a, b) is of the form

$\sf{y - b = {(x - a)}^{2} }$

EVALUATION

Here it is given that the parabola is with vertex at (0, 3)

So the required equation of the parabola is

$\sf{y - 3 = {(x - 0)}^{2} }$

$\sf{ \implies \: y = {x}^{2} + 3}$

FINAL ANSWER

Hence the correct option is

$\sf{4. \: \: y = {x}^{2} + 3 }$