How do you find a quadratic equation if you are only given the solution?
as the solution is at two points? Example
the solution is at x=3 and -6
x=3 and x=-6
x-3=0 and x+6=0
(x-3)(x+6)=0 is the equation, then multiply it out...
x^2+3x -18=0
x3=a2ndx=6
To find a quadratic equation if you are only given the solution(s), you need to know both the x-intercepts of the quadratic equation. The x-intercepts represent the values of x at which the quadratic equation equals zero.
Let's assume you are given the two solutions, x1 and x2. The quadratic equation can be written in the factored form as (x - x1)(x - x2) = 0.
To obtain the standard form of the quadratic equation, you need to expand this factored form by multiplying the two binomials:
(x - x1)(x - x2) = 0
x^2 - x(x2) - x(x1) + x1*x2 = 0
x^2 - (x1 + x2)x + x1*x2 = 0
Therefore, the quadratic equation in standard form is:
f(x) = x^2 - (x1 + x2)x + x1*x2
By substituting the given values of x1 and x2 into this equation, you will have the quadratic equation based on the solutions you were given.