Question 722022: I am having trouble with the following question:if the graph of a quadratic equation has its vertex at the origin, then the related quadratic equation has exactly one solution, tell whether each statement is always, sometimes, or never true. Explain.
I think it's never because there are so many different numbers to use there will be more than one solution; however, I am not sure about this because I don't know how to solve or check this.
Please help me with this problem, and thank you for taking the time to read my question.
Found 2 solutions by josgarithmetic, NR06:
Answer by josgarithmetic(39617)   (Show Source):
You can put this solution on YOUR website! What is the question which you want to evaluate as true or not or to what extent true? You have not shown nor asked it. Distinguish between a quadratic function and a quadratic equation. A quadratic equation can have no or one or two Real solutions. A quadratic function will have a range of values. A quadratic equation which has its vertex on the origin intersects the x-axis in exactly one point; when you solve this equation, you find x=0.
If none of that helps you, then state the exact problem statement completely.
Answer by NR06(1) (Show Source):
You can put this solution on YOUR website! This is the question: "If the graph of a quadratic equation has its vertex at the origin, then the related quadratic equation has exactly one solution. Tell whether this statement is always, sometimes, or never true. Explain." Now, after spending some time thinking about it, i think it is always true because there will be only one zero if the vertex is at the origin. However, I'm not sure if this is right and I'm somewhat confused. Thank you anyways.
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