Question

Question 5 (Essay Worth 6 points)

Part 1:
Solve each of the quadratic equations below and describe what the solution(s) represent to the graph of each. Show your work to receive full credit.

y = x2 + 3x + 2
y = x2 + 2x + 1

Part 2:
Using complete sentences, answer the following questions about the two quadratic equations above.

Do the two quadratic equations have anything in common? If so, what?
What makes y = x2 + 3x + 2 different from y = x2 + 2x + 1?

@radar

Answer 1

The problem does not direct you to solve them by a specific method, so for the first one use the factor method.
y=x^2 + 3x + 2= (x + 2) (x + 1) or x = -2, and x = -1. Now what does this mean? It defines 2 points of the parabola graph. These points are (0,-1) and 0,-2) This is not the only value that x can have. For example x could = 0 and y would then be 2 or (0,2). Solving the quadratic located the "zeroes" or where y=0.

Answer 2

don't forget the vertex point formula b/-2a

Answer 3

ooops change those points to read (-1,0) and (-2,0) Error alert lol

Answer 4

Good point @FriedRice

Answer 5

thanks

Answer 6

The second equation can be solved similarily. And the meanings are similar, obviously the second one will have different value for the "zero roots"

Answer 7

They are both parabolas and they open the same way but cross the x axis at different. The second one has only one x value (-1) therefore it only touches the x axis at one sport and that is the vertex.

Answer 8

Those points should allow you to sketch the curve, and you can always assign velues to x in a table and calculate y. Here is the second equation points plotted: