Question

Please solve with explanation high points

Answer 1

Answer:

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

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

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

Step-by-step 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)

$\frac{-b}{-2}$=3 => b =6

$\frac{-D}{4a}$=$\frac{-b^{2}+4ac}{-4}$ =-3 =>-b^2+4ac=12 => c=-12.