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How can I tell whether a parabola is upward or downward?

Answer
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Hint: This problem deals with determining the shape of the parabola, whether it is upwards or downwards. The general equation of a parabola is x2=4ay where, its vertex is the origin and doesn’t have any intercepts, or y=ax2+bx+c where its vertex may not be the origin, and it has intercepts intersecting the coordinate axes.

Complete step-by-step answer:
We know that the general equation of the parabola is given by: y=ax2+bx+c.
The given parabola is upwards, when a>0 in y=ax2+bx+c. In this case the vertex is the minimum, or lowest point of the parabola. A large positive value of a makes a narrow parabola; a positive value of a which is close to zero makes the parabola wide.
The given parabola is downwards, when a<0 in y=ax2+bx+c. In this case the parabola opens upwards.
The function of the coefficient a in the general equation is to make the parabola wider or skinnier, or to turn it upside down, when a<0, and when the coefficient of x2 is positive, the parabola opens up, otherwise it opens down.

The parabola is upwards when a>0 in y=ax2+bx+c. The parabola is downwards when a<0 in y=ax2+bx+c.

Note:
Please note that the graph of a quadratic function is a U-shaped curve which is a parabola. The sign on the coefficient a of the quadratic function affects whether the graph opens up or down. If a<0, the graph makes a frown (opens down) and if a>0 then the graph makes a smile (opens up).
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