...i need the answer to that too...
If x2 is negative it will have a maximum value If x2 is positive it will have a minimum value
Yes
When the quadratic is written in the form: y = ax2 + bx + c then if a > 0 y has a minimum if a < 0 y has a maximum and if a = 0 y is not a quadratic but y = bx + c, and it is linear. The maximum or minimum is at x = -b/(2a)
Suppose you have a quadratic function of the form y = ax2 + bx + c where a, b and c are real numbers and a is non-zero. [If a = 0 it is not a quadratic!] The turning point for this function may be obtained by differentiating the equation with respect to x, or by completing the squares. However you get there, the turning point is the solution to 2ax + b = 0 or x = -b/2a Now, if a > 0 then the quadratic has a minimum at x = -b/2a and it has no maximum because y tends to +∞ as x tends to ±∞ . if a < 0 then the quadratic has a maximum at x = -b/2a and it has no minimum because y tends to -∞ as x tends to ±∞. You evaluate the value of y at this point. y = a(-b/2a)2 + b(-b/2a) + c = b2/4a - b2/2a + c = -b2/4a + c = -(b2 - 4ac)/4a In either case, if the domain of the function is bounded on both sides, then the missing extremum will be at one or the other bound - whichever is further away from (-b/2a).
maximum and minimum are both (-b/2a , c - (b^2/4a))
It if the max or minimum value.
The minimum is the vertex which in this case is 0,0 or the origin. There isn't a maximum.....
if it opens up then the point is called the minimum if it opens down its called the maximum
In theory you can go down the differentiation route but because it is a quadratic, there is a simpler solution. The general form of a quadratic equation is y = ax2 + bx + c If a > 0 then the quadratic has a minimum If a < 0 then the quadratic has a maximum [and if a = 0 it is not a quadratic!] The maximum or minimum is attained when x = -b/2a and you evaluate y = ax2 + bx + c at this value of x to find the maximum or minimum value of the quadratic.
It can't - unless you analyze the function restricted to a certain interval.
vertex
Standard notation for a quadratic function: y= ax2 + bx + c which forms a parabola, a is positive , minimum value (parabola opens upwards on an x-y graph) a is negative, maximum value (parabola opens downward) See related link.
If x2 is negative it will have a maximum value If x2 is positive it will have a minimum value
Yes
When the quadratic is written in the form: y = ax2 + bx + c then if a > 0 y has a minimum if a < 0 y has a maximum and if a = 0 y is not a quadratic but y = bx + c, and it is linear. The maximum or minimum is at x = -b/(2a)
The vertex.
· whether it is linear, quadratic or exponential · whether it has an upper or lower bound · whether it has a minimum or a maximum value · whether it is constant, decreasing or increasing