Put each in your calculator and check what y equals when x = 90.

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Vocabulary axis of symmetry standard form minimum value maximum value.

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Put each in your calculator and check what y equals when x = 90.

Chapter 2: Functions and Models Lesson 6: Quadratic Models Mrs. Parziale

Vocabulary Quadratic models: models based on quadratic functions

Properties of Quadratics: Parabola opens upward for a>0 (positive) and downward for a<0 (negative). Vertex is the place where the axis of symmetry and the parabola intersect. Vertex is the minimum for a>0 and maximum for a<0

Domain: all real numbers Range: depends on the location of the vertex. (range ≥ min or range ≤ max) The x-intercepts are the solution to f(x) = 0 (done either by factoring or the quadratic formula). The y-intercept is (0, c).

Example 1: Consider f(x) = 2x 2 – 9x + 3 (a) Find its x- and y-intercepts (b) Tell whether the parabola has a maximum or minimum point, and find the coordinates of the vertex.

Example 2: Physics application – Famous quadratic model = Newton’s Formula for Height of an Object Thrown Vertically where g = accel. due to gravity (9.8 for m/s 2 and 32 for ft/s 2 ). A projectile shot from a tower 10 feet high with an upward velocity of 100 feet/second. (a) Approximate the relationship between height (h) in feet and time (t) in seconds after the projectile is shot. (formula) (b) How long will the projectile be in the air?

Example 3: A pizza is sliced by a number of straight cuts as shown below. The table shows the greatest number of pieces f(n) into which it can be sliced by n cuts. a. Fit a quadratic model to these data. b. Use your model to find the greatest number of pizza pieces produced by 5 straight cuts. n01234 f(n)124711

Closure Given the following quadratic function: What is the y-intercept? Does this parabola have a min or max? How do you find the zeros (x-intercepts)? What is the domain? Range?