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Please solve with explanation high points

Please solve with explanation high points-example-1

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Answer:

a. -2x^2 + 3x+5=y

b.-x^2 +5x-4=y

c.-x^2 +6x-12=y

Explanation:

a.y=-2x^2 +bx+c

the points P and Q lie on curve


\left \{ {{-b+c=2} \atop {b+c=8}} \right.

=> b=3, c=5

b. delta = b^2 +4c

x1=
\frac{-b+\sqrt{b^(2)+4c } }{-2} =4

=>
b-\sqrt{4c+b^(2) }=8

x2=
\frac{-b-\sqrt{b^(2)+4c } }{-2}=1

=>2=b+
\sqrt{b^(2)+4c }

suppose :
\sqrt{b^(2)+4c } = a

=>
\left \{ {{a+b=2} \atop {-a+b=8}} \right.

=> a=-3

b=5

a=-3 =>
\sqrt{b^(2)+4c } =-3 => b^2 +4c =9 =>5^2 +4c=9 => c=-4.

c.vertex (3;-3)


(-b)/(-2)=3 => b =6


(-D)/(4a)=
(-b^(2)+4ac)/(-4) =-3 =>-b^2+4ac=12 => c=-12.

User Dharanikesav
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