The product of two consecutive positive integers is 342. represent in the above situation in the form of quadratic equation. find the numbet also.

18 and 19

Step-by-step explanation:

Consecutive positive integers have a difference of 1 between them

let n and n + 1 be the 2 integers, then

n(n + 1) = 342, that is

n² + n = 342 ( subtract 342 from both sides )

n² + n - 342 = 0 ← quadratic equation in standard form

(n + 19)(n - 18) = 0 ← in factored form

Equate each factor to zero and solve for n

n + 19 = 0 ⇒ n = - 19

n - 18 = 0 ⇒ n = 18

However, n > 0 ⇒ n = 18 and n + 1 = 18 + 1 = 19

The 2 integers are 18 and 19

if the eqn of the parabola is f(x) = (x-4)(x+2), we need to mult. this out to find the coordinates of the vertex.

then f(x) = x^2 + 2x - 4x - 8, and f(x) = x^2 - 2x - 8.

one way in which you can find the vertex is to calculate x = -b / (2a).   here, that comes to

        )

x = = 1.   f(1) = 1^2 - 2(1) - 8 = - 9.   vertex is at (1, -9).

        2(1) 

find another point on the curve:   let x=0, for which y=-8.   then (0, -8) is on the curve.   plot the vertex and this point and draw a smooth parabola thru both.

hope this

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