# $

{\text{Write an equation of a horizontal parabola with a vertex of }}\left( { - 1,1} \right){\text{ and a }} \\

{\text{y - intercept of }}\left( {0,2} \right). \\

\\

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Last updated date: 20th Mar 2023

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{\text{Let the equation of the horizontal parabola is }}{\left( {y - h} \right)^2} = 4a\left( {x - k} \right) \\

{\text{because its y intercept is}}\left( {0,2} \right)\;{\text{which is right side of the parabola }} \\

{\text{i}}{\text{.e parabola is opening right side}}{\text{.}} \\

{\text{so the vertex of the parabola is }}\left( {k,h} \right) \\

{\text{So, compare the vertex from the given vertex}} \\

{\text{i}}{\text{.e }}\left( { - 1,1} \right) \\

\Rightarrow k = - 1,\;h = 1 \\

{\text{So, the equation of parabola is}} \\

{\left( {y - 1} \right)^2} = 4a\left( {x + 1} \right) \\

{\text{Now the y intercept is }}\left( {0,2} \right){\text{ which satisfy the parabola}} \\

\Rightarrow {\left( {2 - 1} \right)^2} = 4a\left( {0 + 1} \right) \\

\Rightarrow 1 = 4a \\

\Rightarrow {\text{Equation of parabola is}} \\

{\left( {y - 1} \right)^2} = x + 1 \\

{\text{So, this is your required equation}}{\text{.}} \\

{\text{NOTE: - In this type of problem first check from given condition parabola is opening which side,}} \\

{\text{ then satisfying the condition according to given problem statement you will get your answer}}{\text{.}} \\

$

{\text{Let the equation of the horizontal parabola is }}{\left( {y - h} \right)^2} = 4a\left( {x - k} \right) \\

{\text{because its y intercept is}}\left( {0,2} \right)\;{\text{which is right side of the parabola }} \\

{\text{i}}{\text{.e parabola is opening right side}}{\text{.}} \\

{\text{so the vertex of the parabola is }}\left( {k,h} \right) \\

{\text{So, compare the vertex from the given vertex}} \\

{\text{i}}{\text{.e }}\left( { - 1,1} \right) \\

\Rightarrow k = - 1,\;h = 1 \\

{\text{So, the equation of parabola is}} \\

{\left( {y - 1} \right)^2} = 4a\left( {x + 1} \right) \\

{\text{Now the y intercept is }}\left( {0,2} \right){\text{ which satisfy the parabola}} \\

\Rightarrow {\left( {2 - 1} \right)^2} = 4a\left( {0 + 1} \right) \\

\Rightarrow 1 = 4a \\

\Rightarrow {\text{Equation of parabola is}} \\

{\left( {y - 1} \right)^2} = x + 1 \\

{\text{So, this is your required equation}}{\text{.}} \\

{\text{NOTE: - In this type of problem first check from given condition parabola is opening which side,}} \\

{\text{ then satisfying the condition according to given problem statement you will get your answer}}{\text{.}} \\

$

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