Montana Math MT.CORE.ALG.QUAD.3.a
The Standard
- MT.CORE.ALG.QUAD.3
- Understand that quadratic expressions can be represented in multiple forms and the specific features of each form by: Choosing the form strategically when writing an expression based on given information and intended use, Converting between factored, standard, and vertex forms symbolically and using representations, Understanding the relationship between factored form and the zeros of the function, and Understanding the relationship between vertex form and the vertex of the function.
Understand that quadratic expressions can be represented in multiple forms and the specific features of each form by: Choosing the form strategically when writing an expression based on given information and intended use,
2026 Montana Mathematics Content Standards · Algebraic and Functional Reasoning
Teacher's field guide
What This Standard Means
What Students Need to Do
- Students choose vertex, factored, or standard form based on what they know and what they need to find. They use a known point to find a missing coefficient.
What Mastery Looks Like
- Given a vertex and another point, a student writes an equation in vertex form. Given two zeros and another point, they write it in factored form. They can explain which form shows the peak, zeros, or y-intercept most clearly.
Common Misconceptions
- Students may write (x-3) for a zero of -3 or read the vertex of (x-2)²+5 as (-2, 5). They may set the coefficient in front to 1 without checking a known point.
How to Assess It
- Exit ticket: One parabola has vertex (2, -3) and passes through (0, 5). Another has zeros -1 and 4 and passes through (0, -8). Write each equation in a form that shows the given feature, and name why you chose that form.
Lesson moves
Ways to Teach It
Use algebra tiles to build (x+2)(x+3), expand it, then ask which form shows the zeros and which shows the y-intercept.
Ask students to write two sentences explaining why 2(x-3)(x+1) shows the zeros faster than its expanded form.
Play Form Match with cards showing a vertex, two zeros, or a y-intercept; students match each card to an equation form.
A fountain peaks at (3, 12) and passes through (0, 3); have students write its height equation in a form that shows the peak.
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Related Standards
- MT.7.EE.2
Understand that rewriting an expression in different forms in a problem in context can show how the quantities in it are related.
- MT.CORE.ALG.FUN.3.a
Understanding that different representations highlight different aspects of functions, choosing the representation that is appropriate for the context, and
- MT.PLUS.ALG.POLY.2.a
Choosing the form strategically based on given information and intended use when writing an expression,
- MT.CORE.ALG.LIN.4.a
Choosing the form strategically when writing an equation based on given information and intended use,
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