What is the correct standard form of the equation of the parabola?
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Where the parabola is (-3,2)
To find the correct standard form of the equation of a parabola with vertex (h, k), we need to use the formula:
(x - h)^2 = 4a(y - k)
In this case, the vertex is (-3, 2), so the equation becomes:
(x - (-3))^2 = 4a(y - 2)
Simplifying,
(x + 3)^2 = 4a(y - 2)
And that is the correct standard form of the equation of the parabola with vertex (-3, 2).
The standard form of the equation of a parabola is given by:
y = a(x - h)^2 + k
where (h, k) is the vertex of the parabola and a determines the shape and direction of the parabola.
Given that the vertex is (-3, 2), we can substitute the values of h and k into the equation:
y = a(x - (-3))^2 + 2
Simplifying this equation, we have:
y = a(x + 3)^2 + 2
This is the standard form of the equation of the parabola.