Answer:
2^2 x 5 x 11
Step-by-step explanation:
Take out the common factor
Te x intercepts are where the graph crosses the x axis or wher y=0
the y intercept is where the graph crosses the y axis or where x=0
to find vertex, here is a hack
the x coordinate of the vertex for an equation in form ax^b+bx+c=y is -b/2a
so
y=3x^2+12x+7
-b/2a=-12/2(3)=-12/6=-2
sub that back
y=3(-2)^2+12(-2)+7
y=3(3)-24+7
y=9-17
y=-8
vertex is (-2,-8)
intercepts
x intercept is where y=0
0=3x^2+12x+7
using quadratic formula
x=(-6-√15)/3 and (-6+√15)/3
xints at ((-6-√15)/3,0) and ((-6+√15)/3,0)
yint is where x=0
set x=0
y=7
yint is at y=7 or (0,7)
vertex at (-2,-8)
xints at x=
![\frac{-6+ \sqrt{15} }{3}](https://tex.z-dn.net/?f=%20%5Cfrac%7B-6%2B%20%5Csqrt%7B15%7D%20%7D%7B3%7D%20)
and
![\frac{-6- \sqrt{15} }{3}](https://tex.z-dn.net/?f=%20%5Cfrac%7B-6-%20%5Csqrt%7B15%7D%20%7D%7B3%7D%20)
or at the points
![( \frac{-6+ \sqrt{15} }{3} , 0)](https://tex.z-dn.net/?f=%28%20%5Cfrac%7B-6%2B%20%5Csqrt%7B15%7D%20%7D%7B3%7D%20%2C%200%29%20)
and
![(\frac{-6- \sqrt{15} }{3},0)](https://tex.z-dn.net/?f=%20%28%5Cfrac%7B-6-%20%5Csqrt%7B15%7D%20%7D%7B3%7D%2C0%29%20)
yint at y=7 or at (7,0)
the first one is true and the second one is false
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Answer: </em></h3><h3><em> I think the first answer is S(t) = 2^t - 1 .</em>
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