Algebra 2 Quadratic Functions Review

1. The graphs of the quadratic functions f and g are shown below. y= f x 4 y ( )

0 x -6 -4 -2 0 2 4 6

-2

y= g( x) -4

(a) State the vertex form equations for each function.

(b) Using the quadratic formula, determine the x-value of the points of intersection of the two parabolas. Round off your answers to two places. Your answers should match the graph!

2. Consider the quadratic function Q( x) =( 6x + 54)( 6 - 2x) .

(a) Convert Q( x) to standard form. Then complete the square to convert Q( x) to vertex form.

(b) Solve for x if Q( x) = 200 using any appropriate algebraic method. Round off your answers to two places.

3. Without the help of a calculator, graph each of the following parabolas on the set of axes above.

2 (a) y=2( x - 3) - 3 (b) y= - x2 + 4 (c) y= -2 x2 + 4 x - 3

4. (a) The x-intercepts of the function y 9x  18 10  2x are ______and ______. The y-intercept of the function is ______.

(b) Determine the coordinates of the vertex of the parabola. Show your work clearly.

(d) The standard form equation for this parabola is ______. 5. The subscription to a stock research newsletter costs $500 per year. At present, the newsletter has 4000 subscribers. A survey, done by the company that produces the newsletter, predicts that for every reduction in price of $50, the number of subscribers will increase by 200.

Write a formula for the revenue, R, in terms of x, the number of $50 reductions in price for the newsletter. Then use your formula to determine what the cost of the newsletter should be to maximize revenue for the company. Determine the maximum revenue. Show all your work!

6. (a) Explain clearly what the discriminant is and how it can be used to tell the number of solutions to a quadratic equation.

(b) Write any quadratic equation that has no real roots.

7. (a) Complete the square to determine the vertex of each parabola.

1 (i) y  x2  8x  3 (ii) y x2  4x  2 2

(b) Use your calculator to draw the graphs of the two parabolas from part (a). The points of intersection of the two parabolas are ______and ______. Round all coordinates in your answer accurate to two decimal places. (c) By using algebra, set the equations of the two parabolas equal to each other and determine the exact simplified x-coordinates of the points of intersection of the parabolas. Verify that your answer matches your answers from part (b)!

8. Solve the equation by using factoring.

5 3 x2  3x  2  3 2  x 2   2x

9. (a) If ax2  bx  c  0 , then the quadratic formula states that x  ______.

(b) Find the x-intercepts, accurate to the nearest hundredth, for the parabola y 13x2  8x  8 .

5 89 (c) The two x-intercepts of a parabola are x  . Find the standard form equation of the 4 parabola.

10. Rex launches a model rocket vertically from the roof of a building. The height h, in meters, of the rocket above the ground after t seconds is given by the formula

2 h f t   4.9t  42t  20 .

(a) Determine, using algebra, the time it takes for the rocket to reach its maximum height and state this height.

(b) How high was the building and when will the rocket hit the ground?