Check if the given sequences are quadratic sequences.
7 10 15 22 21 42
The first difference: 3 5 7 1 21.
The second difference: 2 2 6 20.
Since the second difference is not constant, then the given sequence is not a quadratic sequence.
2 9 18 29 42 57
The first difference: 7, 9, 11, 13, 15.
The second difference: 2 2 2 2.
Since the second difference is constant, then the given sequence is a quadratic sequence. Therefore, contains a n2 term.
Let n = 1, 2, 3, 4, 5, 6, ...
Now, let's refer the n2 terms as, 1, 4, 9, 16, 25, 36.
As you see, the terms of the given sequence and n2 terms differ by 1, 5, 9, 13, 17, 21 which is an arithmetic sequence,say {an} with a common difference d = 4 and the first term a = 1. Thus, the nth term formula for this arithmetic sequence is
an = a + (n - 1)d = 1 + 4(n - 1) = 4n - 3.
Therefore, we can find any nth term of the given sequence by using the formula,
nth term = n2 + 4n - 3 (check, for n = 1, 2, 3, 4, 5, 6, ... and you'll obtain the given sequence)
4 15 32 55 85 119
The first difference: 11, 17, 23, 30, 34.
The second difference: 6 6 7 4.
Since the second difference is not constant, then the given sequence is not a quadratic sequence.
5 12 27 50 81 120
The first difference: 7, 15, 23, 31, 39.
The second difference: 8 8 8 8.
Since the second difference is constant, then the given sequence is a quadratic sequence.
I tried to refer the square terms of sequences such as n2, 2n2, 3n2, but they didn't work, because when I subtracted their terms from the terms of the original sequence I couldn't find a common difference among the terms of those resulted sequences. But, 4n2 works. Let n = 1, 2, 3, 4, 5, 6, ...
Now, let's refer the 4n2 terms as, 4, 16, 36, 64, 100, 144.
As you see, the terms of the given sequence and 4n2 terms differ by 1, -4, -9, -14, -19, -24 which is an arithmetic sequence, say {an} with a common difference d = -5 and the first term a = 1. Thus, the nth term formula for this arithmetic sequence is
an = a + (n - 1)d = 1 -5(n - 1) = -5n + 6.
Therefore, we can find any nth term of the given sequence by using the formula,
nth term = 4n2 - 5n + 6 (check, for n = 1, 2, 3, 4, 5, 6, ... and you'll obtain the
given sequence)
Write an algorithm to find the root of quadratic equation
One would use the quadratic formula for solving binomials that are otherwise hard to factor. You can find both real and imaginary solutions using this method, making it highly superior to factoring in this regard.
In a quadratic equation, the vertex (which will be the maximum value of a negative quadratic and the minimum value of a positive quadratic) is in the exact center of any two x values whose corresponding y values are equal. So, you'd start by solving for x, given any y value in the function's range. Then, you'd solve for y where x equals the middle value of the two x's given in the previous. For example:y = x24 = x2x = 2, -2y = (0)2y = 0Which is, indeed, the vertex of y = x2
Chemists use quadratic polynomials constantly in equilibrium calculations. To find unknown concentrations in reactions of that nature. The problem reduces to a polynomial that is solved by the quadratic equation. Simplified answer, Using polynomials it will soon be possible to identify some powerful techniques for seeking out the local extrema of functions, these points or bumps are often very interesting.
look for the interceptions add these and divide it by 2 (that's the x vertex) for the yvertex you just have to fill in the x(vertex) however you can also use the formula -(b/2a)
Write an algorithm to find the root of quadratic equation
To find the roots (solutions) of a quadratic equation.
There are an infinite number of different quadratic equations. The quadratic formula is a single formula that can be used to find the pair of solutions to every quadratic equation.
I suggest you use the quadratic formula.
When an equation cannot be solved for "x" to find the zeroes, the quadratic formula can be used instead for the same purpose.
For any quadratic ax2 + bx + c = 0 we can find x by using the quadratic formulae: the quadratic formula is... [-b +- sqrt(b2 - 4(a)(c)) ] / 2a
No, the quadratic equation, is mainly used in math to find solutions to quadratic expressions. It is not related to science in any way.
In general, quadratic equations have graphs that are parabolas. The quadratic formula tells us how to find the roots of a quadratic equations. If those roots are real, they are the x intercepts of the parabola.
in maths
The quadratic formula is used to find the solutions (roots) of a quadratic equation in the form ax² + bx + c = 0, where "a," "b," and "c" are constants.
Quadratic functions are used to describe free fall.
You substitute the value of the variable into the quadratic equation and evaluate the expression.