Warm Up February , 2014 Use the discriminant to determine the number and type of roots of: a. 2x2 - 6x + 16 = 0 b. x2 – 7x + 8 = 0 2. Solve using the quadratic formula: -3x2 – 8x + 5 = 0 3. Which method would you use to solve this and why? 8x2 - 32 = 0

Writing Quadratics & Systems of Linear/Quad Equations February 21st, 2014 Writing Quadratics & Systems of Linear/Quad Equations

Quick 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

Steps a=___ b=___ c= ___ STAT - #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-put in a table! a = ______ b = ______ c = ________ Equation: (–2, 1), (–1, 0), (0, 1), (1, 4), (2, 9)

You try! a = ______ b = ______ c = ________ Equation:

You try! a = ______ b = ______ c = ________ Equation: (–1, 10), (0, 3), (1, 0), (2, 1)

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

How could you write the equation from looking at the graph? 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

Last year we studied systems of linear equations. We learned three different methods to solve them. Elimination, Substitution and Graphing

Graphing Method To solve is to find the intersections of the graph. Put each in slope intercept form and graph This is what we will use to solve a Quadratic/Linear System

Calculator Notes 1. Type equation 1 = y1, equation 2 = y2 2. Push 2ndTRACE5, move cursor to the left intersection push ENTER 3 times. 3. Push 2ndTRACE5, move cursor to the right intersection push ENTER 3 times.

Example 1-ONE Solution

Example 2-NO solutions

Example 3-INFINITE Solutions

Linear and Quadratic Systems of Equations Today we will learn about systems of quadratic AND linear equations. You can use graphing or substitution

Graphing Method We do this the same way we do linear equations To solve is to find the intersections of the graph.

Graphs & Solutions

How can we CHECK our answers?

Example #2

Example #3:

Substitution Method If we know that y = y Substitution Method If we know that y = y. Then you can set both of the right hand sides of the equations equal.

Example 1: x2 – 4x + 1 = x + 3

Example 2: x + 5 = x2 – 5x + 10

Example #3 –you choose method!

Example #4 – you choose method!

Example #5 – you choose method!

Word Problem Company A: y = x2 – 70x + 3341 Company X: y = 50x + 65 The weekly profits of two different companies selling similar items that opened for business at the same time are modeled by the equations shown below. The profit is represented by y and the number of weeks the companies have been in business is represented by x. According to the projections, what week(s) did the companies have the same profit? What was the profit of both companies during the week(s) of equal profit? Company A: y = x2 – 70x + 3341 Company X: y = 50x + 65

Reasoning The graph at the right shows a quadratic function and the linear function x = b. How many solutions does this system have? Will the number of solutions be the same for any value of b? Explain. If the linear function were changed to y = b, would the number of solutions be the same for any value of b?

Challenge problem for candy! Reasoning What are the solutions of the system y = 2x2 – 11 and y = x2 + 2x – 8? Explain how you solved the system.

Homework Worksheet