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3 years ago

Identify the axis of symmetry and vertex of f(x) = –2x2 –2x–1.

Mathematics

2 answers:

Elena-2011 [213]3 years ago

8 0

Answer:

A. The vertex is at (-0.5, -0.5) and the axis of symmetry is x = -0.5.

Step-by-step explanation:

–2x2 –2x–1

Convert to vertex form:

= -2(x^2 + x) - 1

= -2 [ (x + 0.5x)^2- 0.25] - 1

= -2(x + 0.5)^2 + 0.5 - 1

= -2(x + 0.5)^2 - 0.5.

Compare this with the general vertex form:

a(x - b)^2 + c where the vertex is at (b, c) and the axis of symmetry is

x = b

we see that b = -0.5 and c = -0.5 therefore

the vertex is at (-0.5, -0.5) and the axis of symmetry is x = -0.5.

Marta_Voda [28]3 years ago

4 0

Answer:

The first option

Step-by-step explanation:

Given a quadratic function in standard form : ax² + bx + c : a ≠ 0, then

The equation of the axis of symmetry which is also the x- coordinate of the vertex is found using

x = - $\frac{b}{2a}$

f(x) = - 2x² - 2x - 1 ← is in standard form

with a = - 2, b = - 2, so

x = - $\frac{-2}{-4}$ = - 0.5

Equation of axis of symmetry is x = - 0.5

Substitute x = - 0.5 into f(x)

f(- 0.5) = - 2(- 0.5)² - 2(- 0.5) - 1 = - 0.5 + 1 - 1 = - 0.5

Vertex = (- 0.5, - 0.5 )

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Answer:

$z=-1.28$

And if we solve for a we got

$a=470 -1.28*60=393.2$

So the value of height that separates the bottom 10% (Fastest 10%) of data from the top 90% is 393.2.

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Step-by-step explanation:

Previous concepts

Normal distribution, is a "probability distribution that is symmetric about the mean, showing that data near the mean are more frequent in occurrence than data far from the mean".

The Z-score is "a numerical measurement used in statistics of a value's relationship to the mean (average) of a group of values, measured in terms of standard deviations from the mean".

Solution to the problem

Let X the random variable that represent the time for this event of a population, and for this case we know the distribution for X is given by:

$X \sim N(470,60)$

Where $\mu=470$ and $\sigma=60$

NOTE: For this case the fastest 10% is on the lower tail of the distribution

For this part we want to find a value a, such that we satisfy this condition:

$P(X>a)=0.9$ (a)

$P(X$ (b)

Both conditions are equivalent on this case. We can use the z score again in order to find the value a.

As we can see on the figure attached the z value that satisfy the condition with 0.1 of the area on the left and 0.9 of the area on the right it's z=-1.28. On this case P(Z<-1.28)=0.1 and P(z>-1.28)=0.9

If we use condition (b) from previous we have this:

$P(X$

$P(z$

But we know which value of z satisfy the previous equation so then we can do this:

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And if we solve for a we got

$a=470 -1.28*60=393.2$

So the value of height that separates the bottom 10% (Fastest 10%) of data from the top 90% is 393.2.

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