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2 years ago

The quadratic function in vertex form of a parabola vertex 1,1 and passes through 4,19

Mathematics

1 answer:

Grace [21]2 years ago

5 0

Answer:

y = 2(x - 1)² + 1

Step-by-step explanation:

The equation of a quadratic function in vertex form is

y = a(x - h)² + k

where (h, k) are the coordinates of the vertex and a is a multiplier

Here (h, k) = (1, 1), thus

y = a(x - 1)² + 1

To find a substitute (4, 19) into the equation

19 = a(4 - 1)² + 1

19 = 9a + 1 ( subtract 1 from both sides )

18 = 9a ( divide both sides by 9 ), thus

a = 2

y = 2(x - 1)² + 1 ← in vertex form

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In rectangle KLMN, KM = 10x+24 and KN = 64 find x

pishuonlain [190]

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3 years ago

Determine whether set of values represents an inverse variation. If yes, identify the constant of variation and write an inverse

Natasha_Volkova [10]

SOLUTION

If the table represents an inverse variation, it means that y is inversely proportional to x, written as

$\begin{gathered} y\propto\frac{1}{x} \\ \propto is\text{ a sign of proportionality } \end{gathered}$

Removing the proportionality sign and introducing a constant k, we have

$\begin{gathered} y=k\times\frac{1}{x} \\ y=\frac{k}{x} \end{gathered}$

In the first column, we have x = -4 and y = 3.5. Substituting these values for x and y, we have

$\begin{gathered} y=\frac{k}{x} \\ 3.5=\frac{k}{-4} \\ k=3.5\times-4 \\ k=-14 \end{gathered}$

So, if it's an inverse variation, the relationship would be

$y=\frac{-14}{x}$

In the second column, x = -2 and y = 7.

Now lets substitute the value of x for -2. If we get y to be 7, then the relationship is an inverse variation

We have

$\begin{gathered} y=\frac{-14}{x} \\ y=\frac{-14}{-2} \\ y=7 \end{gathered}$

Since we got y = 7, the relationship is therefore an inverse variation.

The constant k = -14

The equation for the inverse variation is

$y=\frac{-14}{x}$

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10 months ago

Sylvie needs $110 for a concert ticket. She already has $16 and she can earn the rest by working 10 hours at her job. If h repre

oksano4ka [1.4K]

Answer:9.4$ a hour

Step-by-step explanation:

110 - 16 = 94

94 / 10 = 9.4

she makes 9.4$ a hour

<!> Brainliest is appreciated! <!>

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2 years ago

Read 2 more answers

\displaystyle\lim_{ x \rightarrow 0 } \left( \dfrac{ \sqrt[ m ]{ 1+αx \phantom{\tiny{!}}} \times \sqrt[ n ]{ 1+βx \phantom{\tiny

kramer

Answer:

What are you trying to ask.

Step-by-step explanation:

Please Write in a understandable manner.

Thanks from India.

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2 years ago

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Advocard [28]

Answer:

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Step-by-step explanation:

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2 years ago