SOLUTION: Explain how you might go about constructing a quadratic equation whose solutions are -5 and 7. The connection between the graph and the equation is an important and helpful one! B

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Question 716715: Explain how you might go about constructing a quadratic equation whose solutions are -5 and 7.
The connection between the graph and the equation is an important and helpful one! Briefly discuss the effect of the sign of the coefficient a on the graph of y = ax2 + bx + c. Please include two examples of graphs to support your thoughts, one where a < 0 and one where a > 0
I have no idea how to explain or anything. Can someone help please?

Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
+y+=+a%2Ax%5E2+%2B+b%2Ax+%2B+c++
is the general equation for a parabola.
It can either look like a cup that is holding
water ( open up ), or a cup that is
upside down ( open down )
-------------------------
The sign of +a+ tells which it is.
To make it simple, suppose +b+=+0+ and +c+=+0+
Then you have
+y+=+ax%5E2+
Suppose +a+=+3+ ( cup holding water )
Suppose +a+=+-3+ ( cup upside down )
Here is a graph of both these cases:
+graph%28+400%2C+400%2C+-5%2C+5%2C+-5%2C+5%2C+3x%5E2%2C+-3x%5E2+%29+
------------------------------------------
The value of +a determines how fat or skinny
the cup is. large +a+, skinny cup, and
small +a+, fat cup
------------------
The numbers you pick for +b+ and +c+
doesn't change these basic rules. They just move the
graph around the x-y plane.
------------------
Suppose I compare:
+y+=+3x%5E2+%2B+4x+-+1+ and
+y+=+-3x%5E2+%2B+4x+-+1+
You can see they just moved relative to where the vertexes
were at the origin.
+graph%28+400%2C+400%2C+-5%2C+5%2C+-5%2C+5%2C+3x%5E2+%2B+4x+-+1%2C+-3x%5E2+%2B+4x+-+1+%29+
Hope this helps