# algebra

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Find the maximum or minimum of the following quadratic function: y = x2 - x - 56.
A. -56
B. 56
C. -225/4
D. 225/4
d

• algebra -

1. y=x2 - 16

for maximum or minumum, dy/dx=0
hence 2x=0 or x=0

minimum value of function occurs when x=0 which is y=-16

2.using same principle as above,
dy/dx=10x+5

when dy/dx=0 => 10x+5=0 => x=-1/2

minimum value of y= -5/4 - 5/2 + 11

for 3, 4 and 5 use the same principle as 1 and 2

• algebra -

max: infinity (at x=inf)
min: x=1/2, y= you figure it. check sign.

• algebra -

Not sure if you know Calculus, as done by Me

so let's complete the square

y = x^2 - x - 56
= x^2 - x + 1/4 - 1/4 - 56
= (x- 1/2)^2 - 225/4

so we have a min of -225/4 , when x = 1/2

(min because the parabola opens upwards)

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