Montana Math MT.CORE.ALG.QUAD.3.c
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: Understanding the relationship between factored form and the zeros of the function, and
2026 Montana Mathematics Content Standards · Algebraic and Functional Reasoning
Teacher's field guide
What This Standard Means
What Students Need to Do
- Students find the input values that make each factor of a quadratic expression equal zero. They use those values to locate the graph’s x-intercepts and explain why the output is zero there.
What Mastery Looks Like
- Given y = -2(x - 3)(x + 1), a student names 3 and -1 as the zeros and (3, 0) and (-1, 0) as the x-intercepts. They check by substitution and explain that the product is zero when either factor is zero.
Common Misconceptions
- Students may call -3 the zero of x - 3 because they copy the sign inside the factor. They may write (3, 3) instead of (3, 0) for an x-intercept. Some count (x - 3)² as two different intercepts instead of one repeated zero.
How to Assess It
- Exit ticket: For y = 2(x - 3)(x + 1), list the zeros and x-intercepts. Substitute one zero to show why the output is 0.
Lesson moves
Ways to Teach It
Hand out cards labeled x - 3 and x + 1; students place each beside its zero on a desk number line.
Ask students to write why y = 3(x - 2)(x + 4) has zeros 2 and -4, not -2 and 4.
Match cards with factored equations, zero pairs, and x-intercept coordinates; students check each set by substitution.
Use h(t) = -5t(t - 4) for a toy rocket; students find when it reaches the ground and explain each time.
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Related Standards
- 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 writi...
- MT.PLUS.ALG.POLY.2
Understand that polynomial expressions can be represented in both factored and standard form, and the specific features of each form by: Choosing the form strat...
- MT.PLUS.ALG.POLY.2.c
Interpreting the relationship between the factored form of the expression and the zeros of the function.
- MT.CORE.ALG.QUAD.3.d
Understanding the relationship between vertex form and the vertex of the function.
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