SOLUTION: Generate a graph for the following function g(x)=-4x^2 + 16x-19 Find the vertex and x and y intercepts for the graph, show all work

Question 56581: Generate a graph for the following function g(x)=-4x^2 + 16x-19
Find the vertex and x and y intercepts for the graph, show all work
Answer by stanbon(75887) (Show Source): You can put this solution on YOUR website!
g(x)=-4x^2 + 16x-19
Find the vertex and x and y intercepts for the graph
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y-intercept: Let x=0, then g(x)=-19; this is the y-intercept.
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x-intercept: Let g(x)=0, then -4x^2+16x-19=0
x=[-16+-sqrt(256-304)]/-8
x=2+-(1/4)isqrt3]
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To get the vertex:
4x^2-16x+? = -y-19
x^2-4x+? =(-1/4)y-(19/4)
Complete the square to get:
x^2-4x+4=(-1/4)y-19/4 +16/4
(x-2)^2 = (-1/4)y-(3/4)
(x-2)^2 = (-1/4)(y+3)
Vertex at (2,-3)
Cheers,
Stan H.
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