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balandron [24]
2 years ago
7

GCSE maths question about the turning point of the graph. please help!

Mathematics
1 answer:
Neporo4naja [7]2 years ago
6 0

Answer:

The coordinates of the turning point are (2, -9)

Step-by-step explanation:

The coordinates of the turning points of the quadratic equation

y = ax² + bx + c, are (h, k), where

  • h = \frac{-b}{2a}
  • k is the value of y at x = h

∵ The equation of the curve is y = x² + bx + c

→ By comparing it with the form above

∴ a = 1

∵ The point (0, -5) lies on the curve

→ Substitute x by 0 and y by -5 in the equation to find the value f c

∵ -5 = (0)² + b(0) + c

∴ -5 = 0 + 0 + c

∴ -5 = c

→ Substitute it in the equatin

∴ y = x² + bx - 5

∵ The point (5, 0) lies on the curve

→ Substitute x by 5 and y by 0 in the equation to find the value f c

∵ 0 = (5)² + b(5) - 5

∴ 0 = 25 + 5b - 5

→ Add the like terms in the right side

∴ 0 = 20 + 5b

→ Subtract 5b from bth sides

∵ 0 - 5b = 20 + 5b - 5b

∴ -5b = 20

→ Divide both sides by -5 to find b

∴ b = -4

→ Substitute it in the equatin

∴ y = x² - 4x - 5

∵ a = 1 and b = -4

→ Substitute them in the rule of h above t find it

∵ h = \frac{-(-4)}{2(1)} = \frac{4}{2}

∴ h = 2

→ To find k, substitute x by 2 and y by k

∵ k = (2)² - 4(2) - 5

∴ k = 4 - 8 - 5

∴ k = -9

∴ The cordinates of the turning point are (2, -9)

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a famer has 120 feet of fencing with whcih to enclose two adjacent rectangular pens as shown. what dimeensions should be used th
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The dimensions of the rectangular pen should be 15 by 20 feet and the maximum area is 1200 square feet.

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Base = 2x

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∴ y = 2xh

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now we solve for h

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Now we will substitute this value in the above first equation:

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Now for the maximum area we have to find the first order differentiation of y

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At dy/dx = 0 we get the value of x for which y is maximum.

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or, - 16/3 x = -80

or, x = 15 feet

Hence height =  40 - 4/3 x = 40 - 20 = 20feet

Maximum area = 2xh = 2×15×40 = 1200 square feet

The dimensions of the rectangular pen should be 15 by 20 feet and the maximum area is 1200 square feet.

Disclaimer : The missing figure for the question is attached below.

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3 years ago
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Answer:

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Step-by-step explanation:

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Hope this helps :)

5 0
3 years ago
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