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Strike441 [17]
1 year ago
12

Plot the axis of symmetry and the point where the maximum value occurs for this function: h(x) = -(x 2)2 8.

Mathematics
1 answer:
Tpy6a [65]1 year ago
8 0

See attachment for the axis of symmetry and maximum point.

<h3>What is a function?</h3>
  • A function from a set X to a set Y allocates exactly one element of Y to each element of X.
  • The set X is known as the function's domain, while the set Y is known as the function's codomain.
  • Originally, functions were the idealization of how a variable quantity depends on another quantity.

To plot the axis of symmetry:

  • The given function is: h(x) = -(x+2)^{2}  +8
  • This function is in the form: g(x) = a(x-h)^{2} +k
  • Where the axis of symmetry is given by, x = h.
  • y comparison, we have -h=2.
  • This implies h=-2
  • Therefore the axis of symmetry is x = -2.

Therefore, the maximum value occurs at the vertex, given by (h,k)=(-2,8).

So, see attachment for the axis of symmetry and maximum point.

Know more about functions here:

brainly.com/question/25638609

#SPJ4

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(a) Derive an equation of the line passing through the points A(0, 545) and B(4, 726). (Let t be the independent variable and y
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Answer:

The equation of the line is y=45.25t+545

Step-by-step explanation:

The general for of a line is:

y=mt+n       (1)

where:

m is the slope of the line and m is the intercept with the axis of the dependent variable, y in this case.

In order to obtain the value of the slope (m) we can use the corresponding slope formula:

m=\frac{y_{2}-y_1 }{t_2-t_1}         (2)

where t_1, t_2, y_1 and y_2 are the corresponding coordinates of the given points. In this case:

t_1=0\\t_2=4\\y_1=545\\y_2=726\\

Substituting these values in equation (2) we obtain:

m=\frac{726-545}{4-0}=\frac{181}{4}=45.25\\m=45.25

Hence, the line equation is now:

y=45.25t+n     (3)

Now to obtain the value of n you can follow two options:

  1. You can substitute one of your points, A or B, in equation (3). In this way, you will obtain an equation where the variable is n

Note that for this question, it is easier to select point A because of having the independent variable equals to zero t=0. Hence, substituting point A in equation (3):

45.25*0+n=545\\n=545

Therefore, the line equation is: y=45.25t+545

The second option to find n is to think of the meaning of the <em>intercept</em>. The <em>intercept </em>of a line is defined as the point in which the line crosses the axis of the dependent variable, which also means that the value of the independent variable for this point is zero. From this, we could have automatically said that n is equal to 545.

See the attachment for a plot of the line.

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