Warm ups Graph completely (with all parts from worksheet)
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Transcript of Warm ups Graph completely (with all parts from worksheet)
11-2 Solving Quadratic Equations by Graphing
Objective: To find the roots of a quadratic equation.
Standard 21.0
Example 1
Let’s use the warm up problem!
Look at where the parabola crosses the x axis… These points are the ROOTS!
The roots are the x-intercepts. Look at your warmup graph… where does it cross the x axis?
2 2 8y x x
Look at the roots..
How else did we learn how to solve these? Factoring!
2 2 8 0x x
( 4)( 2) 0x x
4 0x 2 0x
{ 4,2}
ROOTS FOR TOO #2 are like this
Does not fall on a nice, whole numberBetween 2 numbers: write as inequality
Start all the way to the left Write with “<“ signs “x” in the middle of the 2 #’s
2 < x < 3
6 < x < 7
TOO – BAD slide.Solve by graphing.
2 2 3 0x x
2 9 5 0x x
2 12 36 0x x
2 2 5 0x x
{ 1,3}
{ 9 8, 1 0}x x
{6, . .}D R
noREALroots
: (1, 4)vertex
: ( 4.5, 15.25)vertex
: (6,0)vertex
Roots
1.
2.
3.
4.
: ( 1, 4)vertex
Estimate if not exact. If not sure if it is exact, then try to factor!
Vertex in on x-axis
Does not cross x-axis
RECAP OF ROOTS
2 Roots Crosses x-axis twice Vertex is below and opens
up Vertex is above and opens
down Whole Numbers
Answer: (x,0) and (x,0) Between 2 Numbers
Answer: # < x < # # < x <
#
1 Root Vertex is on the x-axis Answer is vertex!
(x,0) No Roots
Does not cross x-axis Vertex is above and
opens up Vertex is below and
opens down Answer: None
SIDE NOTE Y-intercept, x always equals 0 so . . .
EX#1 y = 1/2x2 – 2x + 2
y = 1/2(0)2 – 2(0) + 2
y = 0 – 0 + 2
y = 2
(0,2) y-intercept
Y-intercept is ALWAYS “c”
Ex: y = 2x2 – 5x + 26
(0,26)
EX #2 y = -x2 – 2x + 3y = -(0)2 – 2(0) + 3y = 0 – 0 + 3y = 3(0,3) y-intercept
Homework
Pg. 625 # 17-19, 20-23, 35-38 Graph the parabola first, THEN see where it
crosses the x-axis. The point(s) at which it crosses (once, twice, or
none) are the roots. Write the roots in brackets { } Use graph paper!
Homework Groups
Let’s get into the same homework groups that we worked on yesterday.
Once you are seated, raise your hand if you are all finished, or finish, your homework.