Question - Analysis of Quadratic Function Graph Features

To locate minimum Q, the coordinates of vertex \( Q \) of the parabola \( f(x) = ax^2 + bx + c \) can be found by using the vertex formula \( x = -\frac{b}{2a} \). The given equation can be rewritten as \( f(x) = -x^2 + 5 \), therefore we have \( a = -1 \) and \( b = 0 \).

\[ x_Q = -\frac{b}{2a} = -\frac{0}{2(-1)} = 0 \]

To find the y-coordinate of Q, substitute \( x_Q \) into \( f(x) \),

\[ y_Q = f(x_Q) = -x_Q^2 + 5 = -(0)^2 + 5 = 5 \]

Thus the coordinates of Q are \( (0,5) \).

Given that the parabola opens downward (\( a < 0 \)), the vertex is the maximum point P. Therefore, the maximum point P is also at \( (0,5) \).