Part 1)
we have that
F(x) =(x+3)²<span>−1
using a graph tool
see the attached figure N 1
we know that
t</span><span>he x-intercepts of the graph is when y=0
the points are (-4,0) and (-2,0)
</span><span>the y-intercepts of the graph is when x=0
the point is (0,8)
the graph is a vertical parabola that opens up
so
the vertex of the parabola is a minimum
the vertex is the point (-3,-1)
Part 2) </span>Write the function g(x) in the form y=a(x−h)²<span>+k . Write the equation for the line of symmetry for the graph of g(x)
</span>
we have that
G(x) =−2x²<span>+8x+3
</span><span>Group terms that contain the same variable
</span>G(x) =(−2x²+8x)+3
Factor the leading coefficient
G(x) =-2*(x²-4x)+3
<span>Complete the square. Remember to balance the equation
</span>G(x) =-2*(x²-4x+4-4)+3
G(x) =-2*(x²-4x+4)+3 +8
G(x) =-2*(x²-4x+4)+11
the vertex is the point (2,11)
so
the equation for the line of symmetry is x=2
Part 3) we have that
H (t) =−16t²<span>+28t
see the attached figure N 3
</span><span>the total length of time, in seconds, it took the dolphin to complete one jump is the difference for t=0 sec and t=1.75 sec
(1.75-0)=1.75 sec
the answer Part 3) is 1.75 sec</span>
we have that
F(x) =(x+3)²<span>−1
using a graph tool
see the attached figure N 1
we know that
t</span><span>he x-intercepts of the graph is when y=0
the points are (-4,0) and (-2,0)
</span><span>the y-intercepts of the graph is when x=0
the point is (0,8)
the graph is a vertical parabola that opens up
so
the vertex of the parabola is a minimum
the vertex is the point (-3,-1)
Part 2) </span>Write the function g(x) in the form y=a(x−h)²<span>+k . Write the equation for the line of symmetry for the graph of g(x)
</span>
we have that
G(x) =−2x²<span>+8x+3
</span><span>Group terms that contain the same variable
</span>G(x) =(−2x²+8x)+3
Factor the leading coefficient
G(x) =-2*(x²-4x)+3
<span>Complete the square. Remember to balance the equation
</span>G(x) =-2*(x²-4x+4-4)+3
G(x) =-2*(x²-4x+4)+3 +8
G(x) =-2*(x²-4x+4)+11
Rewrite as perfect squares
G(x) =-2*(x-2)²+11
the answer Part 2) is
G(x) =-2*(x-2)²+11
see the attached figure N 2
the vertex is the point (2,11)
so
the equation for the line of symmetry is x=2
Part 3) we have that
H (t) =−16t²<span>+28t
see the attached figure N 3
</span><span>the total length of time, in seconds, it took the dolphin to complete one jump is the difference for t=0 sec and t=1.75 sec
(1.75-0)=1.75 sec
the answer Part 3) is 1.75 sec</span>