The solutions to a quadratic equation are 3/8 and 2/5. Write the quadratic equation in standard form show all appropriate work. (standard equation: f(x)=a(x-h)^2+k)
To write a quadratic equation in standard form "f(x) = a(x - h)^2 + k," we need to determine the values of the variables a, h, and k.
Given that the solutions to the quadratic equation are 3/8 and 2/5, we can start by using the quadratic formula:
x = (-b ± √(b^2 - 4ac)) / (2a)
Since the solutions are 3/8 and 2/5, we can set up two equations using the quadratic formula to find a system of equations:
(-b ± √(b^2 - 4ac)) / (2a) = 3/8 ---- Equation 1
(-b ± √(b^2 - 4ac)) / (2a) = 2/5 ---- Equation 2
Now let's work on simplifying these equations. Since the values mentioned in the quadratic formula are identical, we can equate the two equations:
3/8 = 2/5
To cross-multiply:
3 * 5 = 2 * 8
15 = 16
This equation is not possible, as 15 cannot equal 16. Therefore, there must be an error in the given solutions.
Please double-check the provided solutions and try again with accurate values.