The quadratic function y = - x2 + 10x - 8 models the height of a trestle on a bridge. The x-axis represents ground level. To find where the section of the bridge meets ground level, solve 0 = - x2 + 10x - 8. Where does this section of the bridge meet ground level? Choose an equation that would be used to solve 0 = - x2 + 10x - 8 (x + 25) 2 = - 8 (x - 5) 2 = 17 (x - 10) 2 = 25 Solve the equation to find where the trestle meets ground level. Enter your answers from least to greatest and round to the nearest tenth. The trestle meets the ground at units and units.

Question

Mathematics

Cheeky

3 October, 17:30

The quadratic function y = - x2 + 10x - 8 models the height of a trestle on a bridge. The x-axis represents ground level. To find where the section of the bridge meets ground level, solve 0 = - x2 + 10x - 8. Where does this section of the bridge meet ground level? Choose an equation that would be used to solve 0 = - x2 + 10x - 8 (x + 25) 2 = - 8 (x - 5) 2 = 17 (x - 10) 2 = 25 Solve the equation to find where the trestle meets ground level. Enter your answers from least to greatest and round to the nearest tenth. The trestle meets the ground at units and units.

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Answers (1)

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Julian Khan · Answer 1

The trestle meets ground level at 0.9 units and 9.1 units

Step-by-step explanation:

∵ - x² + 10x - 8 = 0 ⇒ * (-1)

∴ x² - 10x + 8 = 0

∵ 10x/2 = 5x ⇒ (x) * (5) ⇒ square x is x² and square 5 is 25

By using completing square form

∴ (x² - 10x + 25) - 25 + 8 = 0

∴ (x - 5) ² - 17 = 0

∴ (x - 5) ² = 17 ⇒ take square root for both sides

∴ x - 5 = - √17 ⇒ x = - √17 + 5 = 0.9

∴ x - 5 = √17 ⇒ x = √17 + 5 = 9.1

∴ The trestle meets ground level at x = 0.9 and x = 9.1