QUADRATIC RELATIONS
(the x–intercepts)
VERTEX FORM
y = a(x – h)2 + k
STANDARD FORM
y = ax2 + bx + c
NOTE: V(h,k)
NOTE: y–intercept is c
INTERCEPT FORM
y = a(x – r)(x – s)
NOTE: r & s are the x–intercepts
 the intercept form is used to determine the x–intercepts
 the x–intercepts are also called the zeros
 the x-intercepts (or zeros) are the points where the parabola crosses the x–axis
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Example 
State the x and y–intercepts of the relation.
x–intercepts:
______________
y–intercepts:
______________
___________________________________________________________
To determine the x–intercepts from an equation in intercept form,
set each factor to zero and solve for x.
y = 5(x – 3)(x + 5)
Unit 3 Lesson6
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Example 
Determine the zeros of each of the following relations:
a) y = (x + 6)(x – 4)
b) y = –2(x + 2)(x – 2)
c) y = x(x + 5)
d) y = x2 – 12x + 32
e) y = 2x2 + 14x + 24
f) y = –3x2 + 48
Example 
Given the quadratic relation in vertex form, express the relation in
standard form and intercept form.
y = (x – 3)2 – 36
vertex: __________
Example 
a)
y–intercept: __________
x–intercepts: __________
Factor each quadratic relation. Use the factors to determine the zeros.
Then, sketch the graph using the a value to decide if the parabola opens
upward or downward.
y = 4x2 + 4x – 168
y
x
Unit 3 Lesson6
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b)
y = –3x2 + 24x – 48
y
x
c)
y = x2 + 3x + 20
y
x
Example 
Unit 3 Lesson6
A ball was tossed from the roof of a 5m tall building. The path of the
ball can be modelled by the relation, y = –x2 + 4x + 5, where x is the
horizontal distance travelled and y is the height, both in metres.
a)
Express the relation in intercept form.
b)
Determine the zeros of the relation.
c)
State the y–intercept and explain its meaning in this context.
d)
State the horizontal distance at which the ball hit the ground.
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