Question

question
find the coordinates of the vertex of the following parabola algebraically. write your answer as an ((x,y)) point.
(y = -3x^2 + 24x - 45)

Explanation:

Step1: Recall vertex formula for parabola

For a quadratic function \( y = ax^2 + bx + c \), the x - coordinate of the vertex is given by \( x=-\frac{b}{2a} \). Here, \( a=-3 \) and \( b = 24 \).
So, \( x=-\frac{24}{2\times(-3)}=\frac{-24}{-6} = 4 \).

Step2: Find y - coordinate

Substitute \( x = 4 \) into the equation \( y=-3x^{2}+24x - 45 \).
\( y=-3\times(4)^{2}+24\times4-45=-3\times16 + 96-45=-48 + 96-45=3 \).

Answer:

\((4, 3)\)