Question

1. what are the coordinates of the vertex of the graph of $y = x^2 + 14x + 33$?

a $(-16, 7)$
b $(16, -7)$
c $(7, -16)$
d $(-7, -16)$

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, \( a = 1 \), \( b = 14 \), so \( x=-\frac{14}{2\times1}=-7 \).

Step2: Find y - coordinate

Substitute \( x = - 7 \) into the equation \( y=x^{2}+14x + 33 \). Then \( y=(-7)^{2}+14\times(-7)+33=49-98 + 33=-16 \).

Answer:

D. \((-7, -16)\)