The graph of the function h(x) is shown. find the function values h(5), h(7), and h(8)

Function given in the graph is the graph of a quadratic function.

Let the equation of the graphed function is,

Here, is the vertex of the parabola.

From the graph attached,

Vertex of the parabola is (7, 2).

Therefore, equation of the function will be,

Since, (6, 1) is a point lying on the parabola

Therefore, equation of the function graphed will be,

And the function will be,

For

For ,

For

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- 2, 2, 1

Step-by-step explanation:

h(5) means what is the value of y = h(x) when x = 5

The given point indicate the point where x = 5, that is y = - 2

Similarly

h(7) is the point y = h(x) when x = 7

The given point where x = 7 is y = 2

and h(8) is the point y = h(x) when x = 8

The given point where x = 8 is y = 1

Probability = 0.2381

Step-by-step explanation:

A security alarm requires a four digit code by using 0 - 9 and the digits cannot be repeated.

First we calculate how many codes can be made.

Combination =

Where n = 10 and r = 4

=

         =

         = 10 × 9 × 8 × 7

        = 5,040 combinations.

Now we have to find the probability that the code contains only odd numbers. So in 0-9 the odd numbers are = 1, 3, 5, 7, 9

There are 5 odd numbers and we have to make a code of 4 numbers.

Therefore, On first place there are 5 options and in second place 4 options, in third place there are 3 options and in fourth place we have only 2 options.

5 × 4 × 3 × 2  = 120 combinations.

Total combinations of odd numbers are 120.

Then the probability that the code contains only odd numbers is

= 0.0238095 ≈  0.02381

Probability = 0.2381