Page 61 - Math Course 3 (Book 1)

The Quadratic Formula

2
Solve x – 2x – 35 = 0. Round to the nearest tenth if Check the solutions by using the CALC menu on a
necessary. graphing calculator to determine the zeros of the
related quadratic function.
Method 2 Quadratic Formula

2
–b ± b – 4ac
x = Quadratic Formula
2a
2
–(–2) ± (–2) – 4(1)(–35) a = 1, b = –2, and
= c = –35.
2(1)
2 ± 4 + 140
= Multiply. Zero Zero
2 X = –.3145199 X = .84785319
Y = 0 Y = 0
2 ± 144 Add.
= To the nearest tenth, the set is
2 Answer
2 ± 12 {–0.3, 0.8}.
x = 2 Simplify.

2 + 12 2 – 12 Separate the
x = or x = Your Turn!
2 2 solutions.
= 7 = –5 Solve Quadratic Equations

2
Answer The solution set is {–5, 7}. Solve x + x – 30 = 0. Round to the nearest tenth if
necessary.

2
Solve 15x – 8x = 4. Round to the nearest tenth if A. {6, –5}
necessary. B. {–6, 5}
C. {6, 5}
Step 1 Rewrite the equation in standard form. D. Ø

15x² – 8x = 4 Original equation Answer
15x² – 8x – 4 = 4 – 4 Subtract 4 from each side.
15x² – 8x – 4 = 0 Simplify.

Step 2 Apply the Quadratic Formula.

2
–b ± b – 4ac
x = Quadratic Formula
2a Solve 20x – 4x = 8. Round to the nearest tenth if
2
necessary.
2
–(–8) ± (–8) – 4(15)(4) a = 15, b = –8, and
= c = –4
2(15) A. {0.5, 0.7}
B. {–0.5, –0.7}
8 ± 64 + 240 C. {–0.5, 0.7}
= Multiply.
30 D. Ø
8 ± 340 Answer
= Add.
30
Separate the
8 + 304 8 – 304
x = or x = solutions.
30 30
≈ 0.848 ≈ –0.315 Simplify.

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