### Home > CCA2 > Chapter 2 > Lesson 2.1.3 > Problem2-36

2-36.

Find the vertex of each of the following parabolas by averaging the x-intercepts. Then write each equation in graphing form. Homework Help ✎

1. $y=(x−3)(x−11)$

What are the x-intercepts of this equation? After finding them, average the x-coordinates to find the x-value, and then substitute this value into the equation to find the corresponding y-value.

x-intercepts: (3, 0) and (11, 0)
vertex: (7, –16)

equation: $y=(x-7)^2-16$

2. $y=(x+2)(x−6)$

Refer to part (a).

x-intercepts: (–2, 0) and (6, 0)
vertex: (2, –16)

equation: y = (x – 2)2 – 16$y=(x-2)^2-16$

3. $y=x^2−14x+40$

Refer to part (a).

x-intercepts: (10, 0) and (4, 0)
vertex: (7, –9)

equation: $y=(x-7)^2-9$

4. $y=(x−2)^2−1$

First square $(x-2)$ and combine like terms.

Refer to part (a).