5.1 Modeling Data with Quadratic Functions Quadratic Functions Standard Form of a Quadratic Equation: f(x) = ax2 quadratic term + bx + linear term c a≠0 constant term Ex 1) Are the following functions quadratic or linear? a. y = (2x + 3)(x - 4) b. f(x) = 3(x2 - 2x) - 3(x2 - 2) Parabolas Parabola: the graph of a quadratic function Axis of Symmetry: the line that divides the parabola into two parts that are symmetric (mirror images) Vertex: the point where the parabola intersects the axis of symmetry *the y-value of the vertex is the maximum or minimum value of the function Parabolas Ex 2) Identify the vertex of each graph. Is it a maximum or a minimum? Also, identify the points that are symmetric to P and Q. Finding a Quadratic from 3 Points Ex 3) Find the quadratic equation that goes through the points (2, 3), (3, 13), and (4, 29). *We need to find a, b, and c… System of 3 equations: Now try this! – Quadratic Regression Ex 4) The chart below tells us the height of water in mm as it drains from a container over time in seconds. Find the equation of the parabola that best fits this data (use calculator). Time (s) Height (mm) 0 120 10 100 20 83 30 66 40 50 50 37 60 28 HW: 5.1 p. 241 #1-21 odd, 27-29 all, 32, 33 5.1 Modeling Data with Quadratic Functions

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# 5.1 Modeling Data with Quadratic Functions