Question

What’s the equation in vertex form?

Answer 1

`\large\boxed{y=(x+5)^2-64}`

Explanation:

`\text{The vertex form of equation}\ y=ax^2+bx+c:\\\\y=a(x-h)^2+k\\\\h=(-b)/(2a),\ k=f(h)\\\\\text{We have the equation:}\ y=x^2+10x-39\to x=1,\ b=10,\ c=-39.\\\\\text{Substitute:}\\\\h=(-10)/(2(1))=(-10)/(2)=-5\\\\k=f(-5)=(-5)^2+10(-5)-39=25-50-39=-64\\\\\text{Finally:}\\\\y=1(x-(-5))^2-64=(x+5)^2-64`