Question

Write the quadratic function in vertex form. Y = x2 + 16x + 74

Answer 1

Answer-

The vertex form of the given quadratic function is,

$\boxed {\boxed {y = (x+8)^2+10}}$

Solution-

The equation for a parabola or quadratic function can be written in vertex form-

$y=a(x-h)^2+k$

The given quadratic function,

$\Rightarrow y = x^2 + 16x + 74$

$\Rightarrow y = (x)^2 + (2\times x \times \frac{16}{2}) + 74$

$\Rightarrow y = (x)^2 + (2\times x \times 8) + 74$

$\Rightarrow y = (x)^2 + (2\times x \times 8) + (8)^2+74-8^2$

$\Rightarrow y = (x+8)^2+74-64$

$\Rightarrow y = (x+8)^2+10$

This is the vertex form of the given quadratic function with vertex at (-8, 10)