Modeling with Quadratic Functions Answers

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Follow the steps to write the function. 1. Identify x-intercepts: (0, 0) and (5, 0) 2. Use factored form: f(t) = a(t − 0)(t − 5) f(t) = at(t − 5) 3. Find the value of: 12 = a(3)(3 − 5) 4. Write the function: f(t) = t(t −)

An engineer sketches a design for a flashlight that uses a mirror in the shape of a parabola to maximize the output of the light. The function representing the mirror is graphed on the left. Which function models the situation?

Which values complete the function? f(x) = (x – )(x + )

Evaluate Jessica’s work and Sally’s review to determine which statement is true.

An image of a parabolic lens is projected onto a graph. The y-intercept of the graph is (0, 90), and the zeros are 5 and 9. Which equation models the function?

The population, y, of a small town can be represented using a quadratic model. The maximum population, 6,000 people, occurred 20 years after record keeping began. Five years later, the population was 5,950. If x represents the number of years after record keeping began, which equation represents the given scenario?

The curve produced by the water coming from a hose is sketched onto a graph with zeros at 0 and 5. The point (4, 1) also lies on the curve. If h(x) represents the vertical distance from where the water first comes out of the hose and x represents the horizontal distance, which statements are true? Check all that apply.The scenario can be represented by the function h(x) = –0.25(x)(x – 5). The scenario can be represented by the function h(x) = (x)(x + 5).The vertex is on the line x = 2.5.The greatest height that the water reaches is 1.5 units.The scenario can be represented by the function h(x) = –1(x – 5).

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