the answer on the board is = 3
The graph of a quadratic function, like this one, is a parabola. Since the leading coefficient (a) is negative (−2), the parabola opens downward, which means its vertex represents the highest point, or the maximum value.
so to find the maximum/highest value, we must first find the x-coordinate o yung value of x using this formula, but first we must determine the variables of the equation.
-2x^2+4x+1
|
-2 as Variable-A
4 as B
and lastly
1 = C
now to find the value of x-value of the vertex(which is "h")
h=-B/2A so = -4/2(-2) = 1
now after finding the x value ("h") we will now find the y-value which is the maximum/highest point of the parabola using this equation
k= C-Ah^2 (the "^2" means squared there's just no symbol in the keyboard)
k= 1+2(1)^2 = 3
(if you're wondering why the "-A" part became "+2", is because of our variable A which is -2. so the formula became 1-(-2)(1)^2. the "-(-2)" part made the (-2) positive so the formula became "1+2(1)^2" as it is :> )
so now the highest/maximum value of the quadratic function is = 3.
the vertex is = (1,3) btw.