Question

Please solve with explanation high points

Answer 1

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.