Need help identifying the ordered pair(s), vertex, and x intercept.

Question

Quadratic equation is  x^2-18x+72=0. My solution is (x=6, x=12). My instructions are:

1. Graph the quadratic equation, which I have done.

2. Label and include the ordered pair for the vertex on graph.

3. Label and include the ordered pair(s) for the x intercept on the graph. 

 

I'm having difficulty finding/calculating the ordered pair(s). Can anyone help?

Answer 1

 

Hi Michelle,

   Here are some other possible formulas to use for this problem as well.  

 

Vertex Formula:

 

x = -b / 2a

 

Remember (y = ax² + bx + c)

In your equation:

b is -18

a is 1

 

x= - (-18) / 2(1)

x = 18/2

x = 9

 

Plug this in to the original equation (y = x² - 18x +72)

y = (9)² - 18(9) +72

y = 81 - 162 + 72

y = -81 + 72

y = -9

 

Vertex: (9,-9)

 

X-Intercept: (find where y is 0)  If you need help on how I got to this part, let me know.

x² - 18x + 72
(X - 6) (X - 12) = 0

Y is 0 in this case

X - intercepts are where Y = 0

X - 6 = 0
X = 6
X - 12 = 0
X = 12

 

Ordered pairs for X - intercepts:

(6,0) and (12,0)

Answer 2

f(x) = x² - 18x + 72               Use completion of the square

f(x) = x² - 18x + (-9)² + 72 - (-9)²

f(x) = (x - 9)² + 23

 

vertex: (9, 23)

 

The solutions are the x-intercepts: (6, 0), (12, 0).