How do you get the answer and sketch it to this graft
1 answer:
F(x) = -4(x - 2)² + 2 f(x) = -4((x - 2)(x - 2)) + 2 f(x) = -4(x² - 2x - 2x + 4) + 2 f(x) = -4(x² - 4x + 4) + 2 f(x) = -4(x²) + 4(4x) - 4(4) + 2 f(x) = -4x² + 16x - 16 + 2 f(x) = -4x² + 16x - 14 -4x² + 16x - 14 = 0 x = <u>-16 +/- √(16² - 4(-4)(-14))</u> 2(-4) x = <u>-16 +/- √(256 - 224)</u> -8 x = <u>-16 +/- √(32) </u> -8<u> </u>x = <u>-16 +/- 5.66 </u> -8<u> </u>x = <u>-16 + 5.66</u> x = <u>-16 - 5.66 </u> -8 -8<u> </u>x = <u>-10.34</u> x = <u>-21.66</u> -8 -8 x = 1.2925 x = 2.7075 f(x) = -4x² + 16x - 14 f(1.2925) = -4(1.2925)² + 16(1.2925) - 14 f(1,2925) = -4(1.67055625) + 20.68 - 14 f(1.2925) = -6.682225 + 20.68 - 14 f(1.2925) = 13.997775 - 14 f(1.2925) = -0.002225 (x, f(x)) = (1.2925, -0.002225) or f(x) = -4x² + 16x - 14 f(2.7075) = -4(2.7075)² + 16(2.7075) - 14 f(2.7075) = -4(7.33055625) + 43.32 - 14 f(2.7075) = -29.322225 + 43.32 - 14 f(2.7075) = 13.997775 - 14 f(2.7075) = -0.002225 (x, f(x)) = (2.7075, -0.002225) -------------------------------------------------------------------------------------------- f(x) = 2(x - 2)² + 1 f(x) = 2((x - 2)(x - 2)) + 1 f(x) = 2(x² - 2x - 2x + 4) + 1 f(x) = 2(x² - 4x + 4) + 1 f(x) = 2(x²) - 2(4x) + 2(4) + 1 f(x) = 2x² - 8x + 8 + 1 f(x) = 2x² - 8x + 9 2x² - 8x + 9 = 0 x = <u>-(-8) +/- √((-8)² - 4(2)(9)) </u> <u />2(2) x = <u>8 +/- √(64 - 72)</u> 4 x = <u>8 +/- √(-8)</u> 4 x = <u>8 +/- √(8 × (-1))</u> 4 x =<u> 8 +/- √(8)√(-1)</u> 4 x = <u>8 +/- 2.83i</u> 4 x = 2 +/- 1.415i x = 2 + 1.415i x = 2 - 1.415i f(x) = 2x² - 8x + 9 f(2 + 1.415i) = 2(2 + 1.415i)² - 8(2 + 1.415i) + 9 f(2 + 1.415i) = 2((2 + 1.415i)(2 + 1.415i)) - 16 - 11.32i + 9 f(2 + 1.415i) = 2(4 + 2.83i + 2.83i + 2.00225i²) - 16 - 11.32i + 9 f(2 + 1.415i) = 2(4 + 5.66i + 2.00225) - 16 - 11.32i + 9 f(2 + 1.415i) = 8 + 11.32i + 4.0045 - 16 - 11.32i + 9 f(2 + 1.415i) = 8 + 4.0045 - 16 + 9 + 11.32i - 11.32i f(2 + 1.415i) = 12.0045 - 16 + 9 f(2 + 1.415i) = -3.9955 + 9 f(2 + 1.415i) = 5.0045 (x, f(x)) = (2 + 1.415i, 5.0045) or f(x) = 2x² - 8x + 9 f(2 - 1.415i) = 2(2 - 1.415i)² - 8(2 - 1.415i) + 9 f(2 - 1.415i) = 2((2 - 1.415i)(2 - 1.415i)) - 16 + 11.32i + 9 f(2 - 1.415i) = 2(4 - 2.83i - 2.83i + 2.00225i²) - 16 + 11.32i + 9 f(2 - 1.415i) = 2(4 - 5.66i + 2.00225) - 16 + 11.32i + 9 f(2 - 1.415i) = 8 - 11.32i + 4.0045 - 16 + 11.32i + 9 f(2 - 1.415i) = 8 + 4.0045 - 16 + 9 - 11.32i + 11.32i f(2 - 1.415i) = 12.0045 - 16 + 9 f(2 - 1.145i) = -3.9955 + 9 f(2 - 1.415i) = 5.0045 (x, f(x)) = (2 - 1.415i, 5.0045) -------------------------------------------------------------------------------------------- f(x) = -2(x - 4)² + 8 f(x) = -2((x - 4)(x - 4)) + 8 f(x) = -2(x² - 4x - 4x + 16) + 8 f(x) = -2(x² - 8x + 16) + 8 f(x) = -2(x²) + 2(8x) - 2(16) + 8 f(x) = -2x² + 16x - 32 + 8 f(x) = -2x² + 16x - 24 -2x² + 16x - 24 = 0 x = <u>-16 +/- √(16² - 4(-2)(-24))</u> 2(-2) x = <u>-16 +/- √(256 - 192)</u> -4 x = <u>-16 +/- √(64)</u> -4 x = <u>-16 +/- 8</u> -4 x = <u>-16 + 8</u> x = <u>-16 - 8</u> -4 -4 x = <u>-8</u> x = <u>-24</u> -4 -4 x = 2 x = 6 f(x) = -2x² + 16x - 24 f(2) = -2(2)² + 16(2) - 24 f(2) = -2(4) + 32 - 24 f(2) = -8 + 32 - 24 f(2) = 24 - 24 f(2) = 0 (x,f(x)) = (2, 0) or f(x) = -2x² + 16x - 24 f(6) = -2(6)² + 16(6) - 24 f(6) = -2(36) + 96 - 24 f(6) = -72 + 96 - 24 f(6) = 24 - 24 f(6) = 0 (x, f(x)) = (6, 0) <u />
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