Find the equation in STANDARD FORM of the quadratic function that passes through (2,5), if the roots are 1+5 and 1-5
To find the equation in standard form of the quadratic function that passes through the point (2,5) and has roots 1+5 and 1-5, we need to use the fact that the quadratic equation can be written as:
(x - x1)(x - x2) = 0
Where x1 and x2 are the roots.
(x - (1+5))(x - (1-5)) = 0
(x - 6)(x + 4) = 0
Expanding the equation:
x^2 + 4x - 6x - 24 = 0
x^2 - 2x - 24 = 0
Now, we need to substitute the point (2,5) into the equation to find the value of the constant term:
(2)^2 - 2(2) - 24 = 0
4 - 4 - 24 = 0
-20 = 0
Since -20 does not equal 0, the point (2,5) is not a solution of the equation. This means that there is no quadratic function that passes through the point (2,5) and has roots 1+5 and 1-5.