Let y = ax^2 + bx + c for some unknown a, b and c. Write the given conditions as equations in a, b and c. You'll get three equations in three variables. Recall that the point of minimum of a parabola is -b / (2a).
Kindly help me about this quadratic equation please
Q: The quadratic function which takes the value 41 at x=-2 and the value 20 at x=5 and is minimized at x=2 is
y = __x^{2 }- __x + __
The minimum value of this function is __
I really need to solve this . thank you
What will be the equation?
You don't compute an equation; you solve it.
Start by substituting x = -2 into ax^2 + bx + c = 41. Similarly, substitute x = 5 into ax^2 + bx + c = 20. Finally, write the equation saying that the point of minimum, i.e., x = -b / (2a), equals 2.
Hmm, no. The minus in the second equation looks like it acts on 25a only. In any case, -2b - 5b = -7b, so the result should be -21a -7b = 21. You can divide both sides by 7.
I have already said this.
First, it is better to avoid notation spanning several lines because this forum does not preserve alignment. Instead of , you can simply write x = -b / (2a) = 2.
I don't understand the notation "7 [-21a -7b = 21] 7". Dividing -21a - 7b = 21 by 7 gives -3a - b = 3. The last equation, -b / (2a) = 2, can be multiplied by 2a to get -b = 4a, or 4a + b = 0. Thus, you have
Adding these equations gives a = 3. Substituting this value of a into either of the two equations above gives you b, and knowing a and b you can find c from any of the equations in post #5 (with the correction in post #6).