7. Graph

y = x2 - 6x + 5

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

y = 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

0 = x2 - 6x + 5

We need to solve for   x.

Factor

0 = (x - 1)(x - 5)

Set the factors = 0

x - 1 = 0     x - 5 = 0

Solve for   x.

x = 1       x = 5

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

y = x2 - 6x + 5

Add and subtract the square of half of 6.

y = (x2 - 6x + 9) - (9 - 5)

Simplify

y = (x - 3)2- 4

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:

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