1. Solving Quadratic Equations
ALGEBRA 1 LESSON 9-4
Remember
= 6 2. – = –9
3. ± = ± = 1.2
= ± = ±1.1
= 8. ± = ±
9. ± = ± 1 4 1 2 1 9 1 3 49
100 7 10
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2. Solving Quadratic Equations
ALGEBRA 1 LESSON 9-4
Solve each equation by graphing the related function.
a. 2x2 = 0
b. 2x2 + 2 = 0
c. 2x2 – 2 = 0
Graph y = 2x2
Graph y = 2x2 + 2
Graph y = 2x2 – 2
There is one solution, x = 0.
There is no solution.
There are two solutions, x = ±1.
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3. Solving Quadratic Equations
ALGEBRA 1 LESSON 9-4
Solve 3x2 – 75 = 0.
3x2 – = Add 75 to each side.
3x2 = 75
x2 = 25 Divide each side by 3.
x = ± Find the square roots.
x = ± 5 Simplify.
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4. Solving Quadratic Equations
ALGEBRA 1 LESSON 9-4
A museum is planning an exhibit that will contain a large globe. The surface area of the globe will be 315 ft2. Find the radius of the sphere producing this surface area. Use the equation S = 4 r2, where S is the surface area and r is the radius.
S = 4 r 2
315 = 4 r 2
Substitute 315 for S.
Put in calculator ready form.
315
(4)
= r 2
= r 2
315
(4)
Find the principle square root. r
Use a calculator.
The radius of the sphere is about 5 ft.
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5. Solving Quadratic Equations
ALGEBRA 1 LESSON 9-4
1. Solve each equation by finding square roots. If the equation has no solution, write no solution.
a. 2x2 – 8 = 0
b. x2 + 2 = –2
2. Solve each equation by finding square roots.
a. m2 – 25 = 0
b. 49q2 = 9
3. Find the speed of a 4-kg bowling ball with a kinetic energy of 160 joules. Use the equation E = ms2, where m is the object’s mass in kg, E is its kinetic energy, and s is the speed in meters per second. ±2
no solution ±5 3 7 1 2
about 8.94 m/s
9-4