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tensa zangetsu [6.8K]
3 years ago
12

Write the virtud for a parabola that satisfies the condition given. Then write the equation in the form y=ax^2+bc+c. Vertex (3,1

) and a=3 write the equation in the form y=ax^2+bx+c
Mathematics
1 answer:
avanturin [10]3 years ago
8 0

Answer:

  • y = 3(x -3)^2 +1
  • y = 3x^2 -18x +28

Step-by-step explanation:

For vertex (h, k) and vertical scale factor "a", the vertex form of the equation of a parabola is ...

  y = a(x -h)^2 +k

For (h, k) = (3, 1) and a = 3, the equation in vertex form is ...

  y = 3(x -3)^2 +1

__

Expanding this gives the equation in standard form.

  y = 3(x^2 -6x +9) +1

  y = 3x^2 -18x +28

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Let a and b be real numbers satisfying a^3 - 3ab^2 = 47 and b^3 - 3a^2 b = 52. Find a^2 + b^2.
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Answer: a²+b² = -99/2

Step-by-step explanation:

Since we are given two equations, this equations will be solved simultaneously to get a² and b²

a³ - 3ab² = 47 ... 1

b³ - 3a² b = 52... 2

From 1, a(a² - 3b²) = 47...3

From 2, b(b² - 3a²) = 52... 4

Adding 3 and 4, we have;

a²+b²-3b²-3a² = 99 (note that a and b will no longer be part of the equations as they have been factored out)

a²+b²-(3b²+3a²) = 99

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