Question 450628
Putting the quadratic in standard form gives:
f(x) = 1/4(x^2+6x+9) + 7 = 1/4x^2 + 3/2x + 37/4
The x-value of the vertex is -b/2a = (-3/2)/(2/4) = -3
Substitute this value into the original equation to get the y-value of the vertex:
f(x) = y = 1/4(0)^2 + 7 = 7
So the vertex is (-3,7)
The line of symmetry is the vertical line which passes through the vertex:
x = -3
The parabola opens upward so the maximum value is f(x) = {{{infinity}}}
The minimum value is the y-value of the vertex: f(x) = 7
{{{graph(400,400,-20,20,-30,30,1/4*(x+3)^2+7)}}}