Question

Picture inside

Answer 1

@g3n3sis08

Answer 2

Ah, this is much easier. same method

Answer 3

\[y = x ^{2}-12x+12\]
\[y = (x-\frac{ 12 }{ 2 })^{2} -(\frac{ 12 }{2 })^{2}+12\]
\[y = (x-6)^{2}-36+12\]
\[y = (x-6)^{2}-24\]

when x is 6 y is -24.
therefore vertex is ( 6,-24)

Answer 4

\[y = ax^2 + bx +c\]
\[b^2 - 4ac\]

when
\[b^2 -4ac<0\] there are 0 roots
\[b^2-4ac=0\] there is only 1 root
\[b^2 - 4ac>0\] there is more than 1 root.

In quadratic equations
\[b^2 - 4ac>0\] there are 2 roots

roots are point at which the equation meet the x axis

Answer 5

There fore

\[b^2 - 4ac\]
\[(-12)^2 - 4*1*12\]
\[=96\]
\[96>0 \]

so there are 2 roots or 2 points at which the equation meets the x axis