Using the completing-the-square method, rewrite f(x) = x2 − 8x + 3 in vertex form.

1 answer:

8 0

f(x) = x² - 8x + 3
y = x² - 8x + 3
- 3 - 3
y - 3 = x² - 8x + 16
y - 3 + 16 = x² - 8x + 16
y + 13 = x² - 8x + 16
y + 13 = (x - 4)²
- 13 - 13
y = (x - 4)² - 13
f(x) = (x - 4)² - 13

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16) 62.8 m²

17) 19.4 m²

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Step-by-step explanation:

The formula to find area of a circle is: $\pi r^{2}$ . To find radius, find the half of the diameter.

To solve number 16, first find the area of the unshaded circle using the formula: $\pi 4^{2}$ . This is also 3.14*16. Multiply to get 50.24 m². Now find the area of the larger circle using the formula: $\pi 6^{2}$ . This is also 3.14*36. Multiply to get 113.04 m². Now subtract 113.04 - 50.24 to get the shaded area or 62.8 m².

To solve number 17, first find the area of the square using the formula: side x side. In this case multiply: 5.25 x 5.25 to get 27.5625. Round to the nearest tenth to get 27.6 m². Now find the area of the circle using the formula: $\pi 2.625^{2}$ . This is also 3.14*2.625. Multiply to get 8.2425. Round to the nearest tenth to get 8.2. Subtract 27.6 - 8.2 to get 19.4 m².

To solve number 18, find the area of one unshaded circle using the formula: $\pi 1.75^{2}$ . This is also 3.14*3.0625. Multiply to get 9.61625. Round to the nearest tenth to get 9.6 m². Add 9.6 + 9.6 to find the area of both unshaded circles. You get 19.2 m². Now find the area of the shaded circle using the formula: $\pi 6.25^{2}$ . This is also 3.14*39.0625. Multiply to get 122.65625. Round to the nearest tenth: 122.7. Subtract 122.7 - 19.2 to get 103.5 m².