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Write the equation of the parabola with the vertex (2,-2) and passes through (0,-3)

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Answer:

Equation of the parabola: y = -1/4(x - 2)^2 - 2

Explanation:

The vertex form of a quadratic function:

Since we're given the parabola's vertex and a point through which it passes, we can find the equation of the parabola in the vertex form, whose general equation is given by:

y = a(x - h)^2 + k, where:

  • (x, y) is any point on the parabola,
  • a is a constant determining whether the parabola opens up or down,
  • and (h, k) are the coordinates of the vertex.

Finding a and writing the equation of the parabola:

We can find a by substituting (2, -2) for (h, k) and (0, -3) for (x, y) in the vertex form:

-3 = a(0 - 2)^2 - 2

-3 = a(-2)^2 - 2

(-3 = 4a - 2) + 2

(-1 = 4a) / 4

-1/4 = a

Therefore, y = -1/4(x - 2)^2 - 2 is the equation of the parabola with the vertex (2, -2) and that passes through (0, -3).

User Luigi Agosti
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