QUADRATIC RELATIONS
(Solving Problems)
Example 
Given the quadratic relation, y = 2x2 + 20x + 48, state the:
vertex:
______________
x–intercepts:
______________
axis of symmetry:
______________
Does the relation have a maximum
or minimum value?
The maximum or minimum point (vertex) lies halfway between
the zeros (x–intercepts) on the axis of symmetry.
The x–coordinate of the vertex is equal to the x–intercept of the axis of
symmetry. The x–intercept of the axis of symmetry is midway between the
zeros and can be determined by taking the mean of the zeros.
Ex.
How can the y–coordinate of the vertex be determined?
y = 2x2 + 20x + 48
Write the equation of the given quadratic relation in vertex form.
y = a(x – h)2 + k
Unit 3 Lesson 7
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Example 
Given the quadratic relation, y = x2 + 2x – 8:
a) State the y–intercept. ____________
b) Express the equation in intercept form.
y = x2 + 2x – 8
c) State the x–intercepts (zeros). ____________
d) State the equation of the axis of symmetry. ____________
e) State the x–coordinate of the vertex (h value).
Use it to determine the y–coordinate of the vertex (k value).
f) State the vertex. ____________
g) Express the equation in vertex form.
y = x2 + 2x – 8
y
h) Sketch the relation.
x
Unit 3 Lesson 7
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Example 
A football is kicked from the ground level. Its path is given by the relation,
h = –4.9t2 + 29.4t, where h is the football’s height above the ground in
metres and t is the time in seconds.
a) Express the relation in intercept form.
h = –4.9t2 + 29.4t
b) Determine the zeros and the equation of the axis of symmetry.
c) Determine the vertex.
d) Express the relation in vertex form.
h = –4.9t2 + 29.4t
e) Use the above information to answer the following questions:
A. When did the ball hit the ground?
___________________
B. What was the maximum height of the ball?
___________________
C. When did the ball reach its maximum height? ___________________
Homework: p.281–284 #4, 5, 6ace, 14ab, 15
Unit 3 Lesson 7
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