Name: _________________
4.5 Quadratic Equations
Objective: Students will be able to solve quadratic equations by factoring,
taking square roots and by graphing.
Zero Product Property: If ab = 0, then a = 0 or b = 0.
To solve by factoring:
1.) Set the equation equal to 0.
2.) Factor.
3.) Set each factor to 0.
Examples: Solve by factoring.
2.) x2 - 12x - 27 = 0
1.) (x+3)(x-2)=0
Oct 17­7:24 AM
Solve and check by graphing.
3.) 5x2 + 30x + 14 = 2 - 2x
4.) 7x2 - 3x3 = -10x
Oct 17­7:35 AM
1
Brainstorm: Solve. x2 = 25
Examples Solve by taking square roots.
1.) x2 - 49 = 0
2.) 4x2 + 16 = 416
3.) (x+2)2 = 16
4.) 16(x -2)2 = 4
Oct 17­7:38 AM
Application Problems:
1.) A woman drops a front door key to her husband from their
apartment window several stories above the ground. The function
h = –16t2 + 64 gives the height h of the key in feet, t seconds after
she releases it. How long does it take the key to reach the ground?
2.) The graph shows a function modeling the height of one
frog's jump, where x is the distance, in feet, from the jump's
start. How far did the frog jump?
y = -.029x2 + .59x
Oct 17­7:54 AM
2
4.5 Homework
Name: _________________
Solve by factoring.
1.) x2 + 6x + 8 = 0
2.) 4x2 - 49 = 0
3.) 3x2 = x + 4
4.) x2 = -3x + 24x3
Oct 17­8:27 AM
Solve using your calculator.
Recall the steps:
1.) Set the equation = 0.
2.) Go to y = and plug in the equation.
3.) Graph.
4.) Go to 2nd: TRACE: 2:zero.
1.) (1/2)x2 - x - 8 = 0
2.) 5x2 - 7x - 3 = 8
Solve by taking square roots.
2.) 5x2 = 125
1.) x2 = 100
3.) 16x2 - 1 = 120
Oct 17­8:37 AM
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4.) (x - 3)2 = 36
5.) 6(2x+1)2 = 216
6.) Write a quadratic equation (in factored form) whose
solutions are -2, 3 and 4.
Oct 17­8:57 AM
7.) The function h = -16t2 + 1700 gives an object's height h,
in feet, at t seconds.
a.) When will the object be 100 ft above the ground?
(Hint: h = 100)
b.) When will the object be 1000 feet above the ground? Use your
calculator to solve. (Hint: h = 1000)
c.) How long does it take the object to reach the ground? Use your
calculator to solve.
Oct 17­9:55 AM
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