Is the y intercept always the c term after substituting 0 for x?

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Ella - You can always find the y-intercept by setting x equal to zero and solving for y.  For a quadratic function where y=ax^2 +bx +c, the y-intercept will always be equal to c.  But understand that sometimes c might equal zero in which case the y-intercept is simply zero.  A good example is y=x^2.   Try graphing it and see where the y-intercept is.