Question

Determine if (a) 2x^2-x+1 and (b)-x^2-3x-1 has maximum or minimum. Find the x and y values at the max or min pt. for (a) and (b).

Answer 1

f(x) = ax^2 + bx + c

(a) Since a = 2 > 0, parabola opens up, so it will have a minimum. To find the vertex (h,k):
let h = -b/(2a) = -(-1)/(2*2) = 1/4
let k = 2(1/4)^2 - (1/4) + 1 = 7/8
Thus the minimum is at the point (1/4, 7/8).

(b) Since a = -1 < 0, parabola opens down, so it will have a maximum. To find the vertex (h,k):
let h = -b/(2a) = -(-3)/(2*-1) = -3/2
let k = -(3/2)^2-3(-3/2)-1 = 5/4
Thus the maximum is at (-3/2, 5/4).