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Sav [38]
2 years ago
11

Tell whether the set of ordered pairs {(1,1), (3,3), (5,9), (8,13)} satisfies a linear function. Explain

Mathematics
1 answer:
egoroff_w [7]2 years ago
7 0
Hello! In order to find a linear function without graphing it, we can see if the x-values (domain) has more than one value of y (range) out of this set of ordered pairs. Those ordered pairs represent a linear function, because each x-value does not have more than 1 y-value. Therefore, those points satisfies a function.
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goldenfox [79]

Answer: y = -14/9(x + 4)^2 + 7

Step-by-step explanation:

The given roots of the quadratic function is (-1, -7)

The vertex is at (-4, 7)

The formula is

y = a(x - h)^2 + k

The vertex is (h, k)

Comparing with the given vertex, (-4, 7), h = -4 and k = 7

Substituting into the formula

y = a(x - h)^2 + k, it becomes

y = a(x - - 4)^2 + 7

y = a(x + 4)^2 + 7

From the roots given (-1, -7)

x = -1 and y = -7

Substituting x = -1 and y = -7 into the equation,

y = a(x + 4)^2 + 7, it becomes

-7 = a(-1+4)^2 + 7

-7 = a(3^2 ) + 7

- 7 = 9a + 7

-7-7 = 9a

9a = -14

a = -14/9

Substituting a = - 14/9 into the equation, it becomes

y = -14/9(x + 4)^2 + 7

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