Compare functions represented algebraically, graphically, numerically, or verbally.
Decide whether two different representations show the same function
Problem
Do these representations describe the same quadratic function: the equation \(f(x)=(x-2)(x+3)\) and a quadratic graph crossing the \(x\text{-}\text{axis}\) at \(-3\) and \(2\) with \(y\text{-}\text{intercept}\) \(-6\)?
Matching zeros identifies the factors of a quadratic, but it does not yet fix the vertical scale. Write the general factored form with an unknown leading multiplier, then use the y-intercept to determine that multiplier. This checks whether the graph and equation agree as complete functions rather than merely sharing two points.
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