Florida B.E.S.T. MA.912.AR.3.5
The Standard
Given the x-intercepts and another point on the graph of a quadratic function, write the equation for the function.
Florida B.E.S.T. Standards for Mathematics
Teacher's field guide
What This Standard Means
What Students Need to Do
- Students turn each x-intercept into a factor of a quadratic in factored form. They substitute the remaining point to find the leading coefficient, then write and check the equation.
What Mastery Looks Like
- A student writes y = a(x-r₁)(x-r₂) with factors that match the intercepts. The student substitutes the third point, solves for a, and checks the equation against all given points.
Common Misconceptions
- Students often use the wrong sign in a factor, such as writing (x+3) for an intercept at 3. They may assume a equals 1 or substitute the extra point incorrectly.
How to Assess It
- Exit ticket: A parabola has x-intercepts at -2 and 4 and passes through (2, -12). Write its equation and verify all three points.
Lesson moves
Ways to Teach It
Give pairs three point cards; students place them on a coordinate mat, build the factored equation, and test the third point.
Prompt: Why does an x-intercept of 5 create the factor (x-5), and how does the extra point determine vertical stretch?
Run a matching relay with intercept cards, point cards, and equation cards; teams justify each match by solving for a.
Model a kicked ball that lands at 30 meters and reaches (15, 12), then write its height function.
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Related Standards
- MA.912.AR.3.7
Given a table, equation or written description of a quadratic function, graph that function, and determine and interpret its key features.
- MA.912.AR.2.3
Write a linear two-variable equation for a line that is parallel or perpendicular to a given line and goes through a given point.
- MA.912.AR.3.6
Given an expression or equation representing a quadratic function, determine the vertex and zeros and interpret them in terms of a real-world context.
- MA.912.AR.3.4
Write a quadratic function to represent the relationship between two quantities from a graph, a written description or a table of values within a mathematical o...
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