Algebra 2 - NOTES 5-2
Obj: able to solve quadratic equations by graphing by hand or using the graphing calculator
Quadratic Equation in standard form is ax 2 + bx + c = 0 , where a ≠ 0 .
Zero of a Function
Root of an Equation
For a quadratic function y = ax 2 + bx + c , each x-intercept of its graph is a zero of
the function
For the related quadratic equation ax 2 + bx + c = 0 , the x-value of the x-intercept is
a root of the equation, also called a solution to the equation.
Use the related graph of each equation to determine its solutions.
1.
2.
3.
4
Zero(s)________________
Zero(s)_______________
Zero(s)_________________
Roots(solutions) of
x 2 + 3 x − 4 = 0 are_______
Roots(solutions) of
2 x 2 + 4 x + 4 = 0 are_______
Roots(solutions) of
x 2 + 8 x + 16 = 0 are_________
Follow the steps below to solve 0 = x 2 − 25 by graphing the related function f ( x) = x 2 − 25 . `
Find the roots for the equation x 2 − 25 = 0
1.
Clear any equations from Y= and make sure that Plot1 is off.
2.
In Y=, type in the related function x 2 − 25 into Y1.
3.
4.
5.
6.
7.
8.
9.
10.
11.
Press ZOOM, then 6: ZStandard or 0:ZOOMFIT to graph the related quadratic function y = x 2 − 25
IF you do not see the entire parabola, press ZOOM, 3:ZOOM OUT, ENTER, or change the WINDOW settings
Press 2nd TRACE 2:ZERO and you will see a blinking pixel on the graph.
Using the ◄arrow key, move the pixel to the left of an x-intercept, hit ENTER.
Using the arrow key, move the pixel to the right of the x-intercept chosen above, hit ENTER.
Hit ENTER one more time. A blinking pixel will appear on the chosen x-intercept.
The Zero value will appear in the lower left corner.
The value x = 5 is a Zero of the Function f ( x) = x 2 − 25 and a Root of the Equation x 2 − 25 = 0 .
If there is another intercept, follow steps 5 thru 10 for the second intercept.
5.2 Cooperative Learning
DIRECTIONS: With your group, work out the following problems. You need to record answers on your
own page as you work together.
Solve by graphing. Use the Graphing Calculator.
On the homework tonight, Do NOT use the textbook directions [If exact roots cannot be found, state the consecutive integers
between which the roots are located]. Instead, find the answers by graphing on the calculator and finding the zeroes.
1. x 2 = x + 20 (hint: set this equal to zero)
2. x 2 = 4 − 4 x
3. 0 = 2 x 2 − 2 x − 5
Use the formula h(t ) = v 0 t − 16t 2 where h(t) is the height of an object in feet, v0 is the initial velocity in feet per second, and t is
the time in seconds.
4. A tennis ball is hit upward with a velocity of 48 feet per second. Ignoring the height of the tennis player, how long does it take for
the ball to fall to the ground?
h(t)
h(t ) = v 0 t − 16t 2 , but since the velocity is 48 ft/sec, we will use
h(t ) = 48t − 16t 2 So find the zeroes on the TI-83, only one of which is reasonable.
t
I have no clue what to do
even if somebody is
explaining the problem to me
1
What do I still need to work on?
Rate yourself on how well you understood this lesson.
I can do it if someone is
I can kind of do it on my
walking me through the
own, but I need the help of
I can do it on my own
problem
my notes/textbook
2
3
4
I can do it on my own AND I
can explain it to somebody
else
5