Question

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 = x^2 + 3x + 2
y = x^2 + 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 = x^2 + 3x + 2 different from y = x^2 + 2x + 1?

Answer 1

All that can be said to this q is Wolfram is your friend,
First, y =(x+1) (x+2), x=-1 , -2
Second, y = (x+1)^2 = 0, x = -1

Answer 2

y = x^2 + 3x + 2 factorised to

y =(x+2)(x +1)

the parabola is concave up, intercepts the x axis at -2, -1
intercepts the y axis at + 2

has a line of symmetry of x = - 1.5

has a minimum value of y = -1/4

the 2nd curve is

y = x^2 + 2x + 1

factorised is

y = (x +1)^2

the parabola is concave up

has 1 point of contact with the x axis at x = -1

has y intercept at y = 1

the has a lie of symmetry at x = -1

has a minimum value of y = 0

the commonality in the graphs is that they are both

concave up

have a common x intercept of x = -1