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

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) (Show Source): You can put this solution on YOUR website!

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 tells which it is.
To make it simple, suppose and
Then you have

Suppose ( cup holding water )
Suppose ( cup upside down )
Here is a graph of both these cases:

------------------------------------------
The value of determines how fat or skinny
the cup is. large , skinny cup, and
small , fat cup
------------------
The numbers you pick for and
doesn't change these basic rules. They just move the
graph around the x-y plane.
------------------
Suppose I compare:
and

You can see they just moved relative to where the vertexes
were at the origin.

Hope this helps

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