Mississippi Math FA.A.35
The Standard
Use the zeros of a polynomial to construct a rough graph of the function. (A-APR.3)
2025 Mississippi College- and Career-Readiness Standards for Mathematics
Teacher's field guide
What This Standard Means
What Students Need to Do
- Students find the zeros of a polynomial and mark them on the x-axis. They use repeated factors to decide where the curve crosses or touches the axis, then use the leading term to draw the ends.
What Mastery Looks Like
- For y=(x+2)(x-1)^2, a student marks -2 and 1 on the x-axis. Their sketch crosses at -2, touches at 1, falls to the left, and rises to the right.
Common Misconceptions
- Students may draw a crossing at every zero, even when a factor has an even power. They may use the zeros to place the curve but draw the ends in the wrong directions.
How to Assess It
- Ask students to sketch y=(x+1)^2(x-2) on graph paper. Have them label both zeros, show where the curve touches or crosses, and draw both ends.
Lesson moves
Ways to Teach It
Plot the zeros of y=(x+2)(x-1)^2 on graph paper, then bend a pipe cleaner to cross -2, touch 1, and rise right.
Ask: Why does y=(x-4)^2 touch the x-axis at 4 while y=(x-4)^3 crosses there? Sketch both before answering.
Give pairs four factored-polynomial cards and four graph cards to match using zeros, crossings, touches, and tail directions.
Graph a shop's profit model P(x)=-(x-3)(x-8), where x counts hundreds of items sold; mark break-even points and shade profitable sales.
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Printable FA.A.35 Worksheet
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