write the standard form of the equation of the parabola (-3, -2) and a = 5 write the standard form of the equation of the parabola (-3, -2) and a =5
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You should remember that the standard form of equation of parabola is given by `ax^2 + bx + c = y` .
Supposing that the equation provides the vertex `V(-3,-2)` and the leading coefficient `a = 5` , you may write the vertex form of equation of parabola such that:
`y = a(x - h)^2 + k`
h, k are coordinates of vertex of parabola
`y = 5(x + 3)^2 - 2 `
You need to expand the binomial to convert the vertex form of parabola in standard form such that:
`y = 5(x^2 + 6x + 9) - 2 => y = 5x^2 + 30x + 45 - 2`
`y =5x^2 + 30x + 43`
Hence, evaluating the standard form of equation of parabola, under the given conditions, yields `y = 5x^2 + 30x + 43` .
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