Question

# Graph of y = ax^{2} + bx + c = 0 is given adjacently. What conclusions can be drawn from this graph –

- a > 0
- b < 0
- c < 0
- All of the above

Hint:

### So in this question, we have a graph given and we have to do it. As we can see the curve and it is of the parabola and by using the properties of the parabola and its equation, we can answer these questions easily.

## The correct answer is: All of the above

### As we can see from the graph we have a parabola curve and since it is opening in an upward direction. So we can say that a > 0 and

Hence, the option (a) is correct.

Here, we can see that the vertex of the parabola is located in the fourth quadrant , therefore it will be =

On further solving this, we get

Therefore, the option (b) is also correct.

Since, at x=0 , the y intercept will be positive and from this, we can conclude that c < 0 and

Hence, the option (c) will also be correct

On checking all the options, and we can see all options are correct and

Therefore, we conclude that all the options available are correct.

Here we can see that the graph was given to us and us to take out the conclusion from that since we have the options available so I would suggest you to always start to check from the options because by the use of options we can see how easily we concluded this question.

### Related Questions to study

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The number point of intersection between two lines can be counted by finding the number of ways in which two lines can be selected out of the lot as two lines can intersect at most one point.

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The students can make an error if they don’t know about the formula for calculating the number of points as mentioned in the hint which is as follows

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Here we have obtained the total number of 9 digit numbers using the given digits. While finding the number of ways to arrange the odd digits in 5 even places, we have divided the 4! by 2! because the digit 3 were occurring two times and the digit 5 were occurring 2 times. Here we can make a mistake by conserving the number of even digits 4 and the number of odd digits 5, which will result in the wrong answer.

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### The foot of the perpendicular from the point on the line is

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### The sum of all the numbers that can be formed with the digits 2, 3, 4, 5 taken all at a time is (repetition is not allowed) :

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