Question

I need some help, BADLY!


Find the solution(s) to the system. Round answers to the nearest hundredth, if necessary.

y = - 0.5x^2 + x + 6

y = 3.25

Answer 1

I'm unsure what the "Y=3.25" is for..

Answer 2

We got one horizontal line, \(\normalsize\color{blue}{ y = 3.25}\)
And we got an opening down porabola,
\(\normalsize\color{blue}{y = - 0.5x^2 + x \color{red}{-0.5+0.5}+ 6}\)
\(\normalsize\color{blue}{y =\underline{ - 0.5x^2 + x \color{red}{-0.5}}\color{red}{+0.5}+ 6}\)
\(\normalsize\color{blue}{y = - 0.5(x^2 - 2x + 1)+0.5+6}\)
\(\normalsize\color{blue}{y = - 0.5(x - 1)^2+0.5+6}\)
\(\normalsize\color{blue}{y = - 0.5(x - 1)^2+6.5}\)

Answer 3

All you have to do, is to find 2 points that are on y=3.25, if there are any.

Answer 4

Thank you.

Answer 5

Have you found the points ?

Answer 6

Not yet. I'm trying to figure it out..

Answer 7

\(\normalsize\color{blue}{y = - 0.5(x - 1)^2+6.5}\)

\(\normalsize\color{blue}{3.25= - 0.5(x - 1)^2+6.5}\), multiply everything times 4

\(\normalsize\color{blue}{13= -2(x - 1)^2+26}\)

\(\normalsize\color{blue}{-13= -2(x - 1)^2}\)

\(\normalsize\color{blue}{13= 2(x - 1)^2}\)

\(\normalsize\color{blue}{13/2= (x - 1)^2}\)

\(\normalsize\color{blue}{± \sqrt{13/2}= (x - 1)}\)

\(\normalsize\color{blue}{1± \sqrt{13/2}= x }\)

Answer 8

\(\normalsize\color{blue}{1± \sqrt{13/2}= x }\)

\(\normalsize\color{blue}{1± \sqrt{26/4}= x }\)

\(\normalsize\color{blue}{1± \frac{1}{2}\sqrt{26}= x }\)

Answer 9

( ± {1 + ½ √26 } , 3.25 )

Answer 10

-2, 4

Answer 11

Right? @SolomonZelman

Answer 12

No,

( ± {1 + ½ √26 } , 3.25 )
( ± {1 + ½ (5.10) } , 3.25 )
( ± {1 + 2.05 } , 3.25 )
( ± 3.05 , 3.25 )

( 3.05 , 3.25 ) and ( - 3.05 , 3.25 )

Answer 13

Thank you.