Question 56536
I think you forgot an x, so I plugged it in.
Complete the follwing function for {{{g(x)=-4x^2+16x+19}}}  Generate the graph and find the Vertex and x&y intercepts for the graph, show all work. 
Your quadratic equation is in standard form:{{{highlight(f(x)=ax^2+bx+c)}}}.  Your a=-4, b=16, c=19  (note: a is negative, so your parabola opens down.)
First find the axis of symmetry, which is also the x value of the vertex using the formula {{{highlight(x=-b/2a)}}}
{{{x=-(16/(2(-4)))}}}
{{{x=-16/-8}}}
{{{x=2}}}  This is your axis of symmetry and x value of the vertex, to find the y value of the vertex find g(2):
{{{g(2)=-4(2)^2+16(2)+19}}}
{{{g(2)=-4(4)+16(2)+19}}}
{{{g(2)=-16+32+19}}}
{{{g(2)=35}}}
Your vertex is (2,35).  Plot that point.
The y-intercept is found by letting x =0 and solve for y:
{{{g(0)=-4(0)^2+16(0)+19}}}
{{{g(0)=19}}}
The y-intercept is (0,-19).
The x-intercept is found by letting g(x)=0  and solving for x:
{{{0=-4x^2+16x+19}}}
This can't be factored, so use the quadratic formula to solve it:
{{{highlight(x=(-b+-sqrt(b^2-4ac))/(2a))}}}
{{{x=(-(16)+-sqrt((16)^2-4(-4)(19)))/(2(-4))}}}
{{{x=(-16+-sqrt(256+304))/-8}}}
{{{x=(-16+-sqrt(560))/-8}}}
{{{x=(-16+-sqrt(16)*sqrt(35))/-8}}}
{{{x=(-16+-4*sqrt(35))/-8}}}
{{{x=(-16-4*sqrt(35))/-8}}} and {{{x=(-16+4*sqrt(35))/-8}}}
{{{x=-4(4+sqrt(35))/(-4*2)}}} and {{{x=-4(4-sqrt(35))/(-4*2)}}}
{{{x=(4+sqrt(35))/2}}} and {{{x=(4-sqrt(35))/2}}}
x~~4.958039892 and x~~-.9580398915
The program is not responding to my attempts to regraph this.
Plot the vertex(2,35), the y-int (0,19), the x-int (-.95,0) and (4.95,0) and connect the dots.  You should have an upside down parabola.
Happy Calculating!!!