Question 541117: Let f(x)=-x squared+4x+3. What is the y-intercept? What is the graph of f called? Would the vertex be a maximum or minimum value? What is the axis of symmetry? What is the vertex for f? Graph it.
Answer by KMST(5328)   (Show Source):
You can put this solution on YOUR website! 
It intersects/intercepts the y-axis (the line x=0) at a point with  (obviously) and 
The graph is called a parabola.
The leading coefficient in this quadratic function is -1. (The minus sign in front of  is really a -1 coefficient in disguise). In polynomial functions, the coefficient of the highest degree term (that -1 in this case) is called the leading coefficient. Because, compared to the other terms, the absolute value of the term of highest degree grows so fast, it really leads the function wherever it wants to go as x goes to the extremes. While f(x) is 3 at the y-intercept, the leading coefficient wants it to go towards -infinity as x goes to -infinity or to +infinity. So the graph looks sort of like the Gateway Arch of Saint Louis. Function f(x) has a maximum. (If the leading coefficient was positive it would look like a smiley mouth, and would have a minimum).
Your textbook will tell you that a generic parabola of equation  will have an axis of symmetry with equation  .
In your case, a=-1, and b=4, so  .
So the vertex point has  , and  .
The vertex point is (2, 7).
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