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jmc

algebra intermediate

Problem

A parabola has vertex of and has two -intercepts, one positive, and one negative. If this parabola is the graph of which of and must be positive?

Enter the coefficients that must be positive, separated by commas. For example, if you think and must be positive, enter " ", without the quotation marks.
Solution
The -coordinate of the vertex is negative, and there are two -intercepts, so the parabola must be upward facing, which means that must be positive. Furthermore, one -intercept is positive and the other is negative, so the -intercept must be negative.

The -coordinate of the vertex is positive, which is also Since is positive, is negative.

Therefore, the only coefficient that must be positive is
Final answer
a