Mississippi Math FA.F.30
The Standard
Understand the relationship between the constants of a quadratic equation and the attributes of the graph. Recognize the relationship between the value of the discriminant and the type and number of solutions (i.e., predict the characteristics of a graph given the equation).
2025 Mississippi College- and Career-Readiness Standards for Mathematics
Teacher's field guide
What This Standard Means
What Students Need to Do
- Students use a, b, and c to predict a quadratic graph's opening, width, y-intercept, and axis of symmetry. They calculate b²−4ac to predict whether the graph crosses, touches, or misses the x-axis.
What Mastery Looks Like
- Given y=2x²−4x+3, a student identifies an upward-opening graph, a y-intercept of 3, and an axis of symmetry at x=1. They calculate a discriminant of −8 and explain why the graph has no x-intercepts.
Common Misconceptions
- Students may treat c as the x-intercept or use b alone as the vertex's x-coordinate. Some think a zero discriminant means zero roots, rather than one repeated real root. Others say a negative discriminant means no solutions, rather than no real roots.
How to Assess It
- Exit ticket: For y=−x²+6x−9, state the opening, y-intercept, axis of symmetry, and number of real roots. Show the discriminant.
Lesson moves
Ways to Teach It
Plot y=x²−4x+3 and y=x²−4x+5 on graph paper; mark each vertex, y-intercept, and any x-intercepts.
Ask why y=x²−4x+3 and y=2x²−4x+3 have different symmetry lines even though both have b=−4.
Sort cards showing y=x²−4x+3, y=x²−4x+4, and y=x²−4x+5 by the number of x-intercepts.
For h(t)=−5t²+10t+3, find a tossed ball's starting height, peak time, and which zero represents when it lands.
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