Download Ex.1 linear y = 2x+3

Unit 3 ‐ Part 1:
Introduction to Quadratics
• quantitatively identify the basic properties of quadratic relations;
• interpret the zeros of a quadratic relation;
• represent a quadratic relation algebraically in factored and standard form
Relation:
• Gives the relationship between x and y.
• How to get y from x.
• Expressed as an equation involving x, y and coefficients.
• Can be graphed on an xy‐plane.
Ex.1 linear
y = 2x+3
Ex.2 quadratic/parabolic
y = 3x2 ‐ 7x + 5
A relation is linear if the highest exponent (order) is 1.
If the highest exponent (order) of a relation is 2, then it
is a quadratic relation.
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Considering 1st (Δy) and 2nd (Δ2y) differences
Quadratic Relation
Linear Relation
x
y=x+1
x
y
y=x2+1
y
2
y
For quadratic relations, the differences are constant.
For linear relations, the differences are constant.
Ex. Fill in the chart and graph the relation.
x
y= ­2x2­x­1
y
2
The name of the curve of a
quadratic relation is a
parabola.
This graph opens downwards. The second difference
negative.
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Ex. Fill in the chart and graph the relation.
x
y = x2 ­2x­3
y
2
y
4
3
2
1
‐4
‐3
‐2
‐1
‐1
1
2
3
4
‐2
‐3
‐4
This graph open upwards. The second
difference is positive.
The direction of opening of the parabola can be determined from the sign of the 2nd difference (Δy2):
Negative 2nd difference parabola opens down
Positive 2nd difference parabola opens up
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HW: p. 254 # 2abc, 3abc, 4, 5, 8
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