Answer-
The vertex form of the given quadratic function is,
[tex]\boxed {\boxed {y = (x+8)^2+10}}[/tex]
Solution-
The equation for a parabola or quadratic function can be written in vertex form-
[tex]y=a(x-h)^2+k[/tex]
The given quadratic function,
[tex]\Rightarrow y = x^2 + 16x + 74[/tex]
[tex]\Rightarrow y = (x)^2 + (2\times x \times \frac{16}{2}) + 74[/tex]
[tex]\Rightarrow y = (x)^2 + (2\times x \times 8) + 74[/tex]
[tex]\Rightarrow y = (x)^2 + (2\times x \times 8) + (8)^2+74-8^2[/tex]
[tex]\Rightarrow y = (x+8)^2+74-64[/tex]
[tex]\Rightarrow y = (x+8)^2+10[/tex]
This is the vertex form of the given quadratic function with vertex at (-8, 10)
