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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. 1 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. 2 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 3 HW: p. 254 # 2abc, 3abc, 4, 5, 8 4