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)
maximum and minimum are both (-b/2a , c - (b^2/4a))
They are simply referred to as local minimums and maximums. Experience: Algebra 2 Advanced
If x2 is negative it will have a maximum value If x2 is positive it will have a minimum value
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.
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.
The minimum is the vertex which in this case is 0,0 or the origin. There isn't a maximum.....
maximum and minimum are both (-b/2a , c - (b^2/4a))
Apex.
vertex
It can't - unless you analyze the function restricted to a certain interval.
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.
They are simply referred to as local minimums and maximums. Experience: Algebra 2 Advanced
If x2 is negative it will have a maximum value If x2 is positive it will have a minimum value