Math 65 Mod 4. Section 4.1 Solving Quadratic Equations by Graphing and the Square Root Method.
I. Using graphing to solve quadratics:
A. Good visual
B. Good check
C. Caution! Solns are approximate.
D. Steps for solving by graphing:
1. Put equation in Standard Form: 2. Graph the related function: 3. Find where y = 0, the x­intercepts:
Ex. 1: Solve
by graphing. Round to two decimal places.
Use a standard window. Write and graph the related function:
Use to find the zeros, one at a time:
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Ex. 2: Solve by graphing. Round to two decimal places:
a)
b)
c)
II. Solving quadratics using the Square Root Method:
A. This can only be used if there is no ____________
__________ term.
We solve by isolating the __________ ____________ and then
taking the _____________ _____________ of each side.
B. Steps:
1. Isolate the 2. Take 3. Put term
of each side:
in front of 4. Simplify exact or:
Round estimate:
5. Check by graphing:
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Ex. 3: Solve using the square root method. Round answers to two decimal places.
a) b) c) 3
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III. Using quadratics to solve application problems:
The height of a free­falling object is given by the equation:
where
h= height in feet
t= time in seconds
= initial height of object
Ex. 4: How long does it take for a marble to hit the ground when dropped from a window 800 feet above ground? Give both the exact solution and one rounded to two decimal places.
Let's solve it algebraically and check it graphically.
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