Find the coordinates of the​ vertex

Question

Find the coordinates of the vertex, the y-intercept, and the x-intercepts (if any exist) of the following quadratic function.

g(x)=xsquare-4x+21

Answer 1

g(x) = x² - 4x + 21

 

Write this in vertex form.

 

g(x) = (x² - 4x + 4) - 4 + 21

 

g(x) = (x - 2)² + 17

 

 

The vertex is (2, 17).

 

Use this vertex form to find the intercepts.

 

To find x-intercepts, set g(x) = 0 and solve for x.  But, since the vertex is above the x-axis, and the parabola open upward, there are no x-intercepts because the parabola never crosses the x-axis.

 

To find y-intercept, evaluate g(0).