Respuesta :
The axis of symmetry of a parabola is a vertical line that divides the parabola into two congruent halves.
Given quadratic equation have minimum value of -1/8 at x=5/2 .
If a quadratic equation have standard form of [tex]y = ax^2 + bx + c[/tex], where a, b, and c equal all real numbers. We can use the formula [tex]x = -b / 2a[/tex] to find the line of symmetry.
[tex]h(x)=1/2(3-x)(2-x)\\\\h(x)=\frac{1}{2} x^2-\frac{5}{2}x+3[/tex]
Here, a=1/2 , b= -5/2 and c=3
So, line of symmetry [tex]x=\frac{-(-5/2)}{2(1/2)} =5/2[/tex]
[tex]h(5/2)=1/2(3-5/2)(2-5/2)\\\\=1/2*(1/2)(-1/2)\\=-1/8[/tex]
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