Graph each quadratic function and identify its key characteristics. f(x) = x^2 - 2x - 3

See graph

Step-by-step explanation:

We want to graph the function .

Let us rewrite this function in the vertex form so that we can graph it easily.

We achieve this by completing the square as follows;

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Comparing to  ,  we have ,this means the graph will open up.

where is the vertex of the quadratic graph.

To find the y-intercept we put into the function to get,

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To find the x-intercept, we put .

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With the nature of graph in mind, taking into consideration, the vertex and the intercepts, we draw the graph to obtain the quadratic graph in the attachment.

the solution of the equation is 2.23 ⇒ answer b

step-by-step explanation:

* lets revise the meaning of exponential function

- the form of the exponential function is y = ab^x, where a ≠ 0, b > 0 ,  

  b ≠ 1, and x is any real number

- it has a constant base b

- it has a variable exponent x

- to solve an exponential equation, take the log or ln of both sides,  

  and solve for the variable

* lets solve the problem

∵

- the base is 7 and the exponent is x

- insert ㏑ in both sides

∴

- use the rule

∴ x ㏑(7) = ㏑(77)

- to find x divide both sides by ㏑(7)

∴

* the solution of the equation is 2.23 to the nearest 2 decimal places

they would have to work 32 hours.