Question 864226: I really need help with this quadratic equation. I have a project and my teacher doesn't explain the information needed. The equation is: x^2-14x+24. I have to graph it and find the following: roots, y-intercept, axis of symetry, and vertex. I don't understand any of it. Please help!
Answer by ankor@dixie-net.com(22740)   (Show Source):
You can put this solution on YOUR website! The equation is: x^2 -14x + 24.
I have to graph it
Construct the graph using the following points, find y, a typical table
x | y
-------
0 | 24
2 | 0
7 |-25
12| 0
13| 11
Should look like this
:
find the following:
roots,
The roots are the x intercepts (occur when y=0)
You can see on the graph, the roots are x=2 and x=12
You can also find the roots by factoring the equations
x^2 - 14x + 24 can be factored to (x-12)(x-2), x = 12,2
:
y-intercept,
This is easy, occurs when x=0
y = 0^2 - 14(0) + 24
x = 24
:
axis of symmetry, and vertex.
The axis of symmetry can be found using the formula x --b/(2a), where
a = 1; b = -14
x = 
x = 14/2
x = 7 is the axis of symmetry
Find the vertex, replace x with 7 and find y
y = 7^2 - 14(x) + 24
y = 49 - 98 + 24
y = -25
7, -25 is the vertex
:
all this should be apparent on the graph
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