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We are given with a quadratic equation which represents a Parabola , we need to find the vertex of the parabola , But let's recall that , For any quadratic equation of the form ax² + bx + c = 0 , the vertex of the parabola is given by ;
Where , D = b² - 4ac (Discriminant)
Now , On comparing the given equation with ax² + bx + c , we have
⇢⇢⇢ <em><u>a = 1 , b = - 10 , c = 2</u></em><em><u>7</u></em>
Now , Calculating D ;
Now , Calculating the vertex ;
Hence , The vertex of the parabola is at (5,2)
Note :- As the Discriminant < 0 . So , the equation will have imaginary roots .
Refer to the attachment for the graph as well .
This is a geometric sequence, with the first term: 1/64
The common ratio is found through the ratio of the first two terms and the second and third term.
Since there is a common difference of 2, we can generalise this sequence to find the nth term:
a is the first term, r is the common ratio, and n is the nth term in the sequence.
Substituting n = 7, we get:
Thus, the next term in the sequence is 1.
The common ratio is found through the ratio of the first two terms and the second and third term.
Since there is a common difference of 2, we can generalise this sequence to find the nth term:
a is the first term, r is the common ratio, and n is the nth term in the sequence.
Substituting n = 7, we get:
Thus, the next term in the sequence is 1.