Question 994539

Say whether the graph of the equation y=-x^2+4x-1 opens up, down, left, or right.Give the coordinates of the vertex and the equation of the axis of symmetry.Write your quadratic function in vertex form. Find the maximum or minimum value.  Explain how you can determine this value.
<pre>{{{y = - x^2 + 4x - 1}}}
{{{highlight_green(y = - (x - 2)^2 + 3)}}} ----- Completed the square to obtain equation in vertex form
Opens concave down since the coefficient on {{{x^2}}} is < 0
Coordinates of the vertex: ({{{2}}}{{{","}}}{{{3}}})
Equation of the axis of symmetry: {{{highlight_green(x = 2)}}}
Maximum value, or y-coordinate of vertex: {{{y = - (2)^2 + 4(2) - 1}}}, or {{{highlight_green(y = 3)}}}