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What are all the intercepts of the graph of...? (6 Problems)

20. At what points does the graph of

y = x^2 - 3x -10 cross the x-axis

21. What are all of the intercepts of the graph of

y = 15x^2 + 89x - 6?

22. What are all the intercepts of the graph of

y = 2x^2 - 11x + 5?

23. What are all the intercepts of the graph of

y = 6x^2 + 13x + 6?

24. What are all the intercepts of the graph of

y = x^2 + x + 5?

25. What are all the intercepts of the graph of

y = x^3 - x?

Solution Preview

Hello and thank you for posting your question to Brainmass.

Intercept is a point when one of the values (x or y) in the coordinate (x,y) is zero.
If the value of x is zero, then the point is on the y axis (y intercept) - for example (0,2)
If the the value of y is zero than the point in on the x axis (x intercept) - for example (3,0)

20. At what points does the graph of

y = x^2 - 3x -10 cross the x-axis

When the line crosses the x axis, the value of y in the coordinate is zero. Then we get the equation:

0=x^2-3x-10

solving:

0=x^2+2x-5x-10
0=x(x+2)-5(x+2)
0=(x-5)(x+2)

We have two possible solutions: x=5 and x=-2
Thus we have two points where y=0: (5,0) and (-2,0)

21. What ...

Solution Summary

Intercepts are found. The solution is detailed and well presented. The response was given a rating of "5/5" by the student who originally posted the question.

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