How do you find the maximum/minimum of a quadratic relation if it has no roots/zeros?

Question

Can you please explain with details?

Answer 1

Hello,
For ax^2+bx+c.

To find the x-value of the turning point (max/min) you can use
x = -b/(2a). Then put this x-value into the relation to find the y-value.

For example.

y = 2x^2-3x+3.

the x-value of the turning point (vertex) = -(-3)/(2*2) = 3/4.

Now put this into the equation y = 2(3/4)^2 -3(3/4) +3 =
2(9/16) - (9/4) +3 =
(18/16) -(36/16) + 3 =
-(18/16) + 3 =
-(18/16) + (48/16) =
30/16 = 15/8 or 1 and 7/8 .

So we have the min. since it opens upward at.

(3/4,15/8)

Hope this helps!!

Answer 2

+x² => min and -x² =>max

STEP 1 Find dy/dx

STEP 2 Solve dy/ dx = 0 ( usually factorise )


STEP 3 Find y value .

STEP 4 Higher y value => MAX. Lower y value => MIN.