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ruslelena [56]
3 years ago
13

I provided the answers I just need you to show work. I’ll even mark you the Brainliest!

Mathematics
1 answer:
Sindrei [870]3 years ago
6 0

The intercepts and the graph on your worksheet are not correct. Please see below for details:

x^2-2x-3=0 has solutions at x=-1 and x=3 (use the quadratic formula to solve). That means these are the x-intercepts, namely points:

(-1,0) and (3,0).

The y-intercept comes from setting x=0 and calculating the y value:

y=0^2-2\cdot0-3=-3

so the y-intercept is (0,-3).

Now to the graph: Based on the form of the function we can see this is a quadratic function and its graph will be a parabola. You can reformat the expression in the following form

y = x^2-2x-3=(x-1)^2-4

and that will indicate that the apex of the parabola (open up) will be at the point (1,-4).

Knowing the apex, the x intercepts, and the y intercept, we can graph it now.

Graph is in the image attached.

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How many points on the graph represent a relative minimum? please help
Tasya [4]
<h3>Answer:  1</h3>

Point B is the only relative minimum here.

===========================================================

Explanation:

A relative minimum is a valley point, or lowest point, in a given neighborhood. Points to the left and right of the valley point must be larger than the relative min (or else you'd have some other lower point to negate its relative min-ness).

Point B is the only point that fits the description mentioned in the first paragraph. For a certain neighborhood, B is the lowest valley point so that's why we have a relative min here.

There's only 1 such valley point in this graph.

--------------

Side notes:

  • Points A and D are relative maximums since they are the highest point in their respective regions. They represent the highest peaks of their corresponding mountains.
  • Points A, C and E are x intercepts or roots. This is where the graph either touches the x axis or crosses the x axis.
  • The phrasing "a certain neighborhood" is admittedly vague. It depends on further context of the problem. There are multiple ways to set up a region or interval of points to consider. Though visually you can probably spot a relative min fairly quickly by just looking at the valley points.
  • If you have a possible relative min, look directly to the left and right of this point. if you can find a lower point, then the candidate point is <u>not</u> a relative min.
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