SOLUTION: (m-1/4)^2=49/16

Question 818393: (m-1/4)^2=49/16
Answer by TimothyLamb(4379) (Show Source): You can put this solution on YOUR website!
(m - 1/4)^2 = 49/16
(m - 1/4)(m - 1/4) = 49/16
mm - 1/2m + 1/16 = 49/16
mm - 1/2m + 1/16 - 49/16 = 0
mm - 1/2m - 48/16 = 0
mm - 1/2m - 3 = 0
m^2 - 0.5m - 3 = 0
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the above quadratic equation is in standard form, with a=1, b=-0.5, and c=-3
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to solve the quadratic equation, by using the quadratic formula, plug this:
1 -0.5 -3
into this: https://sooeet.com/math/quadratic-equation-solver.php
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the two real roots (i.e. the two solutions), of the quadratic are:
m = 2
m = -1.5
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the quadratic vertex is a minimum at: ( m= 0.25, f(m)= -3.0625 )
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the axis of symmetry is: x = 0.25
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the directrix is: y = -3.3125
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