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tamaranim1 [39]
3 years ago
9

Quadratic equation whose vertex is (2,3) and y intercept is 11

Mathematics
1 answer:
never [62]3 years ago
5 0

Answer:

y = 2(x - 2)² + 3      vertex form

y = 2x² - 8x + 11     standard form

Step-by-step explanation:

Vertex form

y = a(x - h)² + k

(h, k) = (2, 3)

y = a(x - 2)² + 3

To find "a" plug in the y-intercept (0, 11)

11 = a(-2)² + 3

11 = 4a + 3

Subtract 3 from both sides

8 = 4a

a = 2

y = 2(x - 2)² + 3

Expand

y = 2(x² - 4x + 4) + 3

y = 2x² - 8x + 11

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Answer:

\boxed{121\:  is \:  a \: perfect \: square}

Step-by-step explanation:

the \:  \sqrt[3]{121}  \: is \: not \: a \: perfect \: cube \\ but \\ the \:  \sqrt{121}  = 11 \to \: is \: a \: perfect \: square \\

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2 years ago
The relation ((6, 8), (7, 10), (7, 12), (8, 16),
Brilliant_brown [7]

Answer:

x = 7 is repeated twice.

Hence, there is NO MORE unique input. We can not have repeated inputs.

Thus, the relation is NOT a function.

Step-by-step explanation:

Given the relation

  • {(6, 8), (7, 10), (7, 12), (8, 16), (10, 16)}

We know that a relation is a function that has only one output for any unique input.

As the inputs or x-values of the relations are:

at x = 6, y = 8

at x = 7, y = 10

at x = 7, y = 12

at x = 8, y = 16

at x = 10, y = 16

If we closely observe, we can check that there is a repetition of x values.

i.e. x = 7 is repeated twice.

Hence, there is NO MORE unique input. We can not have repeated inputs.

Thus, the relation is NOT a function.

8 0
3 years ago
The scale of a model is 0.5in : 6 ft. find the length of the model for an actual length of 204 ft
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2 years ago
Lins father is paying for a $20 meal. He has a%15 off coupon for the meal. After the discount, a 7% sales tax is applied. What d
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Step-by-step explanation:

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Answer:

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Step-by-step explanation:

9-5=9x-6x

Combine like terms

4 = 3x

We can solve for x

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4/3 = 3x/3

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