quadratic systems - ms. taylor's math class
Post on 07-Apr-2022
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1. 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
4. Solve using the square root method (2x-1)2 = 6
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)
EXAMPLE
� The following data forms a parabola, what are the
roots? Find the equation.
x y
-4 8
-3 0
-2 -6
0 -12
4 0
5 8
HOW COULD YOU WRITE THE EQUATION FROM
LOOKING AT THE GRAPH?
� Find the zeros, write out the factors, and multiply out!
�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.
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.
+−=
+=
14
3
2xxy
xy
SUBSTITUTION METHOD
�If we know that y = y. Then you
can set both of the right hand
sides of the equations equal.
+−=
+=
14
3
2xxy
xy
WORD PROBLEM
� 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.
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