Math 148
Lab 2
Quadratic Equations
Due: Wednesday, April 12
Directions: Work out each problem in the space provided on the answer sheet and write
your answer clearly on the answer line. Submit the answer sheet to your recitation
instructor.
Material from this lab will appear on the first midterm.
Purpose: If you know two, three, four, etc. points on the graph of a line, you can
determine the equation of the line. But, one point is not enough! You need at least
two points to determine the equation of the line. How many points on the graph of
a quadratic are needed to determine the equation of the quadratic?
There are different forms of the equation of a line. You should be familiar with the
following two forms:
•y=mx +b(Slope-Intercept Form)
•y−y◦=m(x−x◦) (Point-Slope Form)
Depending on the information provided, one form is a better choice than the others.
For the equation of a quadratic, you also have a choice of different forms. In this
lab you will work with the following forms:
•y=ax2+bx +c(Standard Form)
•y=C(x−z1)(x−z2) (Factored Form)
•y=A(x−h)2+k(Vertex Form)
Warm Up Exercises:
Example Suppose the point (2,15) lies on the graph of y=ax2+ 6x+ 13 where ais an
unknown constant. Find a.
Solution: Because the point (2,15) is on the graph of y=ax2+ 6x+ 13,the point (2,15)
satisfies the equation y=ax2+ 6x+ 13.That is, when x= 2, y = 15.So, plug x= 2
and y= 15 into y=ax2+ 6x+ 13,and then solve for a:
15 = a(2)2+ 6(2) + 13
15 = 4a+ 25
−10 = 4a
−2.5 = aor a = -2.5
Now you try:
1. Suppose (5,18) lies on the graph of y=ax2+ 3x+ 2.Find a.
2. Assume that the graph of y=C(x−2)(x+ 5) contains the point (8,12).Find C.
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