An expression is shown below:
f(x) = 2x² - x - 5
Part A: What are the x-intercepts of the graph of f(x)? Show your work (2
points)
Part B: Is the vertex of the graph of f(x) going to be a maximum or minimum?
What are the coordinates of the vertex? Justify your answers and show your
work. (3 points)
Part C: What are the steps you would use to graph f(x)? Justify that you can
use the answers obtained in Part A and Part B to draw the graph. (5 points)
(10 points)

answer:

Part A: The x intercepts are x coordinate that yield an output of zero:

We can use the quadratic formula to solve this equation:

So, the two solutions are

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So, the graph of the function passes trough the points (1, 0) and (3/2, 0)

Part B: A quadratic equation  always represents a parabola. The parabola is facing up (it's "U" shaped) if a is positive, while it faces down ("n" shaped) if a is negative. In this case a is positive, so the vertex is a minimum.

We can find the x coordinate of the vertex using the formula

And plug that value to find the y coordinate:

Part C: We already did pretty much everything we could have done to plot the graph. We know the vertex and the x-intercepts, so you know that the parabola will have to pass through those points. Remember that the vertical axis of symmetry passes through the vertex, and if you want you can sample some more point to be more accurate.

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Step-by-step explanation:

p ÷ r = tan(x)

step-by-step explanation:

given that there is a figure below shows a right triangle: a right triangle is shown with hypotenuse equal to q units and the length of the legs equal to p units and r units.

graph is missing so i will create the graph as per given information.

the angle between the legs having lengths p units and q units is y degrees. the angle between the legs having lengths r units and q units is x degrees.

now we need to find about what is p ÷ r equal to.

so we can use trigonometric ratio tan(x)=[altitude]/[base] to find the value of p ÷ r, because p is the altitude and r is the base.

p ÷ r=tan(x)

hence final answer is p ÷ r=tan(x).