Question

question 10 of 10
what is the vertex of the graph of the function below?
y = x² + 10x + 24
a. (-4, 0)
b. (-4, -1)
c. (-5, 0)
d. (-5, -1)

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 \( x=-\frac{b}{2a} \). In the function \( y = x^2+10x + 24 \), \( a = 1 \), \( b = 10 \), and \( c=24 \).
So, \( x=-\frac{10}{2\times1}=- 5 \).

Step2: Find the y - coordinate of the vertex

Substitute \( x=-5 \) into the function \( y=x^2 + 10x+24 \).
\( y=(-5)^2+10\times(-5)+24 \)
\( y = 25-50 + 24 \)
\( y=-1 \)

Answer:

D. \((-5, -1)\)