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{\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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Answer
367.8k+ views
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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{.}} \\
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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{.}} \\
$
Last updated date: 22nd Sep 2023
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