In your own words, answer the following:· Without solving or looking at a graph, how do you know if a quadratic equation will have one, two, or no solutions? (3 pts)· How do you find a quadratic equation if you are only given the solution? Demonstrate with an example how to create a quadratic equation given its solution(s). Make sure to explains all steps. (4 pts)· Is it possible to have different quadratic equations with the same solution? Explain and include an example. (2 pts)· Provide your classmate’s with one or two solutions with which they must create a quadratic equation. (1 pt)
a. First, put the equation in standard form of ax²+bx+c=0. If b²<4ac, there are no solutions. If b²=4ac, there is one solution. If b²>4ac, then there are two solutions.b. When given x=a and x=b, the original equation is (x-a)*(x-b) = x²-ax-bx+ab = x²-(a+b)x+abc. No. (x-a)*(x-b) can only simplify to x²-(a+b)x+ab. a+b=b+a and ab=ba, so even doing the math in the other order makes no difference.d. x=5 or x=-3, x=-2 or x=4, x=4 or x=3
oops. for c, include x=6 or x=-2, (x-6)(x+2) = x²-6x+2x-12 = x²-4x-12, no matter how you do the math.
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