advertisement

Algebra 2 Notes – Lesson 5.2 1. Properties of Parabolas Remember the standard form for a quadratic function: 𝑓(𝑥) = 𝑎𝑥 2 + 𝑏𝑥 + 𝑐 When 𝒂 > 𝟎 The parabola opens _____________________. The vertex is a _______________________. When 𝒂 < 𝟎 The parabola opens ___________________. The vertex is a _______________________. 2. Important Points of a Parabola The y – intercept of the function happens when _____________________________________. The equation for the line of symmetry is _________________________. This equation also gives you ____________________________________________________. To find the y-value of the vertex, plug in the number you found for x and solve for y. **THE VALUE OF THE MAXIMUM/MINIMUM IS GIVEN BY THE Y-VALUE OF THE VERTEX** Examples: Find the vertex and the y-intercept of each quadratic equation. Use those points to graph the function (reflect to get the other points!) a) 𝑦 = 𝑥 2 − 2𝑥 − 3 b) 𝑦 = −𝑥 2 + 4𝑥 + 2 8 8 6 6 4 4 2 2 -8 -7 -6 -5 -4 -3 -2 -1 1 2 3 4 5 6 7 8 -8 -7 -6 -5 -4 -3 -2 -1 -2 -2 -4 -4 -6 -6 -8 -8 1 2 3 4 5 6 7 8 Algebra 2 Notes – Lesson 5.2 c) 𝑦 = 𝑥 2 + 3 d) 1 𝑦 = − 4 𝑥 2 + 2𝑥 8 8 6 6 4 4 2 2 -8 -7 -6 -5 -4 -3 -2 -1 1 2 3 4 5 6 7 8 -8 -7 -6 -5 -4 -3 -2 -1 -2 -2 -4 -4 -6 -6 -8 -8 1 2 3 4 5 6 7 8 e) Your small business determines that profits are maximized with the following equation: 𝑦 = −2𝑥 2 + 15𝑥 + 5 x = workers employed y = profit (in thousand $) What number of workers will give the company the MOST profit (maximum)? What is that profit? f) A lighting fixture manufacturer has daily production of 𝐶 = 0.25𝑛2 − 10𝑛 + 800, where C is the total daily cost in dollars and n is the number of light fixtures produced. How many fixtures should be produced to yield a minimum cost?