Lesson 5
The x-Intercepts of a Quadratic Relation
Factor.
x
2
+ 15x + 36
x
2
– 5x - 14
5x
2
+ 30x - 135
Compare the Equation of a Quadratic Relation to Its Graph
1.
a)
Graph the quadratic relation y = x
2
+ 10x + 16.
What are the x-intercepts?
a)
Factor the expression on the right side of the equal sign.
b)
Compare the x-intercepts to the constant terms on the binomial factors of the factored
form of the relation (in the brackets).
What do you notice?
c)
Graph the factored relation in Y
2
.
What do you notice?
2.
Complete the table.
Find the x-intercepts without graphing.
Relation
Factored Form
x-Intercepts
y = x
2
+ 10x + 21
y = x
2
– 8x + 15
y = x
2
+ 2x - 24
y = x
2
- 49
3.
Graph each factored relation from Question 2.
Use the graphs to find the x-intercepts.
How do these x-intercepts compare to those you found in question 2?
4.
Reflect.
Given a quadratic Relation in the form y = x
2
+ bx + c, how can you find the x-
intercepts without graphing?

Intercept form
of a quadratic relation is y = a(x – r)(x – s).
In some other textbooks, you
may see it written as y = a(x – s)(x – t).

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- Fall '14
- Been
- Graph Theory, Equals sign, ASCII