Warm Up x2 + 2x + 4 = 0 2x2 + 3x - 5 = 0 x2 - 2x + 8 = 0

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Presentation transcript:

Warm Up x2 + 2x + 4 = 0 2x2 + 3x - 5 = 0 x2 - 2x + 8 = 0 Solve the quadratics using the quadratic formula: x2 + 2x + 4 = 0 2x2 + 3x - 5 = 0 x2 - 2x + 8 = 0

Quiz Review: What is the x-value? Time or Height? What is the y-value? How do you find the maximum? How do you find when the projectile hits the ground? How do you find the time of a certain height? How do you find the height at certain time? How do you find the initial height?

Quiz Review: American astronauts working on a space station on the moon toss a ball into the air. The height of the ball is represented by the equation h(t) = -2.7t2 + 13.5t + 14, where t represents time in seconds since the ball was thrown and h(t) represents the height of the ball in feet. What is the maximum height of the ball and how long did it take to reach that height? When did the ball come back down and hit the ground? What was the initial height of the ball? At what time did the ball reach a height of 20 feet? How high was the ball after 1.4 seconds?

Quiz Review The profits of Mr. Unlucky’s company can be represented by the equation y = -3x2 +18x – 4, where y is the amount of profit in hundreds of thousands of dollars and x is the number of years of operation. He realizes his company is on the downturn and wishes to sell before he ends up in debt. a. When will Mr. Unlucky’s business show the maximum profit? What is the maximum profit? b. At what time will it be too late to sell the business? (When will the company make no money and start to approach debt?)

Quiz Review The profits of Mr. Unlucky’s company can be represented by the equation y = -3x2 +18x – 4, where y is the amount of profit in hundreds of thousands of dollars and x is the number of years of operation. He realizes his company is on the downturn and wishes to sell before he ends up in debt. c. What will the profit be after 1 year in operation? d. What was the initial profit that the company was making at the beginning?

Warm Up Solve by factoring: x2 + 4x + 3 = 0 2. 2x2 + 5x - 12 = 0 3. 2x2 + 4x + 6 = 0

Writing Quadratics October 13th

Review

Given the points….find the equation! Sometimes we will be given data in a table or a list of points and asked to write the equation. Here are the steps to do just that …

Steps to find: a =___ b =___ c = ___ STAT (next to the left arrow) - #1 Edit Enter X values in L1 Enter Y values or f(x) in L2 STAT CALC CALC - #5 QuadReg Go down to Calculate Put in the “a” “b” “c” values to form a quadratic

Example #2 a = ______ b = ______ c = ________ Equation: Put these values into the table: (-2, 1), (–1, 0), (0, 1), (1, 4), (2, 9)

Example #3 – You try! a = _____ b = _____ c = _____ Equation:

Example #4 The following data forms a parabola. First, what are the roots? Also, find the equation! x y -4 8 -3 -2 -6 -12 4 5

Find the zeros, write out the factors, and multiply out! Looking at the graph … How could you use the graph of a quadratic function to write the equation for the quadratic? Find the zeros, write out the factors, and multiply out!

Example: What if the parabola opens down?

You try! Find the equation!

Writing the Equation If the equation does not have whole number zeros, you can always make a table of points from the graph and find the Quadratic Equation of best fit using “QuadReg” on the calculator (like we did on the first slide!)

What are the roots of this graph? Example: Find the equation of the given quadratic: What are the roots of this graph?

Challenge Problem