7. Graph

a) What is the *y*-intercept?

b) What are the *x*-intercepts?

c) What are the coordinates of the vertex?

a) The y-intercept is the point where the graph crosses the *y* axis. Its *x*-coordinate is 0. If we set *x* = 0 in our equation we get

*y* = (0)^{2} - 6(0) + 5
= 0 - 0 + 5

b) The *x*-intercept is the point where the graph crosses the *x* axis. Its *y*-coordinate is 0. If we set *y* = 0 in our equation we get

We need to solve for *x.*

Factor

Set the factors = 0

Solve for *x.*

c) To find the coordinates of the vertex, we first transform the equation into vertex form.

Add and subtract the square of half of 6.

Simplify

To get the coordinates of the vertex:

Change the sign on the number inside the parentheses to get the *x*-coordinate

Don't change the sign on the number outside the parentheses to get the *y*-coordinate.

The vertex is at (3, -4)

Plot these points and the graph will look like: