
How can I tell whether a parabola is upward or downward?
Answer
467.7k+ views
Hint: This problem deals with determining the shape of the parabola, whether it is upwards or downwards. The general equation of a parabola is where, its vertex is the origin and doesn’t have any intercepts, or 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: .
The given parabola is upwards, when in . 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 in . In this case the parabola opens upwards.
The function of the coefficient in the general equation is to make the parabola wider or skinnier, or to turn it upside down, when , and when the coefficient of is positive, the parabola opens up, otherwise it opens down.
The parabola is upwards when in . The parabola is downwards when in .
Note:
Please note that the graph of a quadratic function is a U-shaped curve which is a parabola. The sign on the coefficient of the quadratic function affects whether the graph opens up or down. If , the graph makes a frown (opens down) and if then the graph makes a smile (opens up).
Complete step-by-step answer:
We know that the general equation of the parabola is given by:
The given parabola is upwards, when
The given parabola is downwards, when
The function of the coefficient
The parabola is upwards when
Note:
Please note that the graph of a quadratic function is a U-shaped curve which is a parabola. The sign on the coefficient
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