### Home > INT3 > Chapter 2 > Lesson 2.1.1 > Problem2-7

2-7.

Determine the vertex of each of the following parabolas by averaging the $x$‑intercepts. Then write each function in graphing form.

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: $y = (x - 7)^2 - 16$

1. $y = (x + 2)(x - 6)$

Refer to part (a).

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

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

1. $y = x^2 - 14x + 40$

Refer to part (a).

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

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

1. $y = (x - 2)^2 - 1$

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

Refer to part (a).