Question

The general form of an parabola is 4y2+40y+3x+103=0. What is the standard form of the parabola?

Answer 1

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Answer:

  x = -4/3y² -40/3y -103/3

  x = -4/3(y +5)² -1

Step-by-step explanation:

Solve for x.

  x = (4y² +40y +103)/(-3)

  x = -4/3y² -40/3y -103/3 . . . . 'standard form' in the US

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Taking our clues from the graph*, we can write the vertex form equation as ...

  x = -4/3(y +5)² -1 . . . . . . 'standard form' in other places

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* The vertex is (-1, -5), so for some leading coefficient, the equation will be ...

  x = a(y -(-5))² +(-1) = a(y +5)² -1

The value of 'a' is the scale factor. Here, that is the difference between the parabola value (x = -2 1/3) and the vertex value (x = -1) one unit away from the vertex.