Quadratic Functions Review Sheet

Advanced Topics Review Sheet

Parabolas

I. For each of the following parabolas, find the x-intercepts, the y-intercept, the axis of symmetry and the vertex. 1. ^ = 2^-5^ + 3 3. y=(2-x)(2 + x) 2.

= ~3

+l 2 + 8

•

4. y = xz-6x

II. Given the parabola y = 2x2 + Sx + kor what values of k will the parabola have: a.) 2 x-intercepts b.) 1 x-intercept c.) no x-intercepts III. Find the equation of the parabola given the following points: 1. (4,0), (8,0), and (0,6)

2. vertex (-2,3) y-intercept 4

IV. For each of the following, find an equation for the quadratic function described: 1. The function f has zeroes -3 and 2 and f(0)= 1. 2. The maximum value of the function occurs at g(2) = 5 and g(0) = 1. 3. The function f is tangent to the x-axis at (-3,0) with y-intercept 2. V. Find the point(s) of intersection for each of the following: l.y = * 2 -5* + 6 2. y = (2x-9)(3-2x) x + y-2 y=10

3. .y = -*2 +4* + l 2x-y=-2

VI. Word Problems: 1 . From the center of the 20 yd (60 foot) line, a football player attempts to make a field goal by kicking the ball directly toward the goal posts, which are 90 feet away. The goal post crossbar is 10 feet above the ground. The ball reaches its highest altitude of 38 feet at a point 45 feet from where it was kicked. a. Make a sketch showing the path of the football. If the point from which the ball is kicked is the origin of a coordinate system, find an equation of the parabolic path of the football. b. Will the kicker make the field goal? VII. Max-Min Problems 1 . Find 2 numbers with sum 1 5 whose product is as great as possible (a maximum). 2. A pen is to be built along a wall from 56 meters of fencing. Determine the value of x that will maximize the area to be enclosed. 3. A manufacturer charges $24 for stereo headphones and has been selling 1000 of them per week. He estimates that for every $ 1 price reduction, 1 00 more headphones can be sold per week. What price for the headphones will maximize his total profit?