Question

What is the vertex of the graph of the function below?
y = x2 +10x + 24

Answer 1

`\huge\boxed{(-5,\ -1)}`

Explanation:

`\text{The vertex form of a quadratic equation}\ y=ax^2+bx+c:\\\\y=a(x-h)^2+k\\\\\text{where}\ (h,\ k)\ \text{is a vertex},\ \text{and}\ h=(-b)/(2a),\ k=f(h).`

`\text{We have}\ y=x^2+10x+24\to a=1,\ b=10,\ c=24.\\\\\text{Substitute:}\\\\h=(-10)/(2(1))=(-10)/(2)=-5\\\\k=f(-5)\to\text{put}\ x=-5\ \text{to the equation}:\\\\k=(-5)^2+10(-5)+24=25-50+24=-1\\\\\text{The vertex}:\ (-5,\ -1)`