Write a quadratic equation given two solutions

It's We need to check another point. Another way of saying this is that the x-intercepts are the solutions to this equation.

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So if b squared minus 4ac is equal to 0, you only have one solution. That's the only solution to this equation. So b squared minus 4ac is minus Conclusion: Working backward will create an equation, but remember that there are other equations that will also have that same set of solutions.

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Page 1. What's 4 times 49? Negative b is negative 14 over 2 times a. But what I want to do here is actually explore the quadratic formula, and think about how we can determine the number of solutions without even maybe necessarily finding them explicitly.

write a quadratic equation given two solutions

Since 0, is on this graph, it will satisfy the equation of the graph. And negative b is-- we could just solve it.

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So 49 times 4. The "solutions" of an equation are also the x-intercepts of the corresponding graph. Negative b is negative 14 over 2 times a. Also, the "2a" in the denominator of the Formula is underneath everything above, not just the square root. It determines the number of solutions we have. If b squared minus 4ac is greater than 0, what's going to happen? So let's think about it in the context of this equation right here. In the equation ,a is the coefficient of the term, b is the coefficient of the x term, and c is the constant. And we know, from dealing with real numbers, you can't take the square root. If this b squared minus 4ac is a positive number-- so let's think about this a little bit.

So it's equal to negative 7. The answers are 1 and These answers may or may not be solutions to the original equations.

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Quadratic Equations