NAME _________________________________
GEOMETRY
UNIT 9
Graphing Parabolas and Circles
Date
Page
3/15
2,3
3/18
3/19
4
3/20
3/21
5,6
3/22
7
3/25
8
3/26
3/27
Topic
Homework
Solving Quadratic/Linear systems
graphically
Practice
Quiz
Solving Quadratic/Linear systems
algebraically
Equations of Circles & Graphing
More Circles
Quiz
Equations of circles using points on a
diameter.
Find the intersection of circles and
linear or quadratic equations
Review
Test
1
Worksheet (need graphing
calculator)_
No homework
No Homework
Practice sheet 12-5
No Homework
Worksheet
Worksheet
STUDY!
Enjoy your break
QUADRATIC LINEAR SYSTEMS
Review questions:
1.) What does the graph of a linear equation look like?___i_______________
2.) What is the general form of a linear equation?________=________________
3.) What does the graph of a quadratic equation look like?___smile/frown_________________
4.) What is the general form of a quadratic equation?____y=𝑥 2 + 𝑏𝑥 + 𝑐__________________
Sometimes the parabola opens up…
Sometimes the parabola opens down…
Y=+𝑥 2
y= -𝑥 2
5.) If you graph a quadratic/linear system, you are graphing a ___line____________ and a _qudratic_______
together and finding the points of intersection. There can be at most _____3_________ solutions.
Draw: One solution:
two solutions:
no solutions:
Solving system of equations
Identify each equation as a linear or quadratic equation. Using your graphing calculator, sketch the graph of
each equation and show all work. Identify the solution set.
1.) y=x+2 ____________________
y=
____________________
2
2.) y=
_____________________
y=2 ________________________
3.) What is the solution of the following system of equations?
y = (x + 3)2 − 4
y = 2x + 5
A) (0, −4)
B) (−4, 0)
C) (−4, −3) and (0, 5)
D) (−3, −4) and (5, 0)
3
SOLVING QUADRATIC LINEAR SYSTEMS ALGEBRAICALLY
1.) Without graphing, tell if the point (3,-1) is a solution to the following system of equations?
Y=-x2+x+4
Y=x-4
STEPS TO SOLVING ALGEBRAICALLY:
1.) Solve both equations for y.
2.) Set the equations equal to each other.
3.) Move everything to one side of the equation and get zero on the other side.
4.) Factor.
5.) Set each factor equal to zero and solve for x.
6.) Plug x back into one of the original equations to find y values.
1.) Find the solutions for the system of equations:
Y=x2+5x-45
Y+10=3x
4
EQUATION OF A CIRCLE
General equation of a circle ______________________________
Radius =
Center Point =
Find the center point and radius:
1.)
c.p.(
,
) r:
2.)
c.p.(
,
) r:
3.)
c.p.(
,
) r:
4.)
c.p.(
,
) r:
Write the equation given the following information
Center point Radius
5.)
(13,-7)
6
6.)
(4,0)
1
7.)
(-1,1)
8.)
(0,0)
Equation
9
9.) (7,3) diameter: 8
5
1.)Graph the circle
3.) Write the equation of the circle
GRAPHING CIRCLES
2.) Graph the circle:
(x-3)2+y2=36
4.)Write the equation of the circle.
6
FINDING CENTER, RADIUS OF A CIRCLE GIVEN POINTS
1.) a.) Draw a circle whose center point is (3,4) and passes through the origin.
b.) What is the radius?
c.) Write the equation:
d.)Is the point (-1,7) on the circle?
Show algebraically
2.) A circle is drawn so that the points A(-2,4) ,B(4,-4) are the endpoints of the diameter. Graph and write an
equation for the circle
3.) The midpoint of the diameter of a circle is (-5, 6) and a point on the circle is (-2,1).
a.) graph the circle
b.) find the radius:
c.) write the equation of the circle.
d.) find the other endpoint of the diameter.
7
INTERSECTIONS OF LINES, CIRCLES AND PARABOLAS
1.) Graph and find the points of intersection for the circle and the line below:
(x-5)2+(y+3)2=9
Y=x-5
2.) On the set of axes below, graph the system of equations. How many solutions are there? Show,
algebraically that the point (0,-2) is a solution to the system of equations.
(x+3)2+(y-2)2=25
2y+4=-x
3.) State the solutions to the following system of equations:
x2+(y+4)2=16
x=-4
What kind of line is x=-4?
8