Answer:
The y-value of the vertex is 49
Step-by-step explanation:
The given quadratic function is
[tex]y=-x^2-10x+24[/tex]
We complete the square to find the vertex.
First factor [tex]-1[/tex] from the first two terms.
[tex]y=-(x^2+10x)+24[/tex]
Add and subtract the square of half the coefficient of x.
[tex]y=-(x^2+10x+5^2-5^2)+24[/tex]
[tex]y=-(x^2+10x+5^2)--5^2+24[/tex]
Recognize the perfect square trinomial.
[tex]y=-(x+5)^2+25+24[/tex]
[tex]y=-(x+5)^2+49[/tex]
The function is now of the form;
[tex]y=a(x-h)^2+k[/tex], where (h,k)=(-5,49) is the vertex.
The y-value of the vertex is 49
