Montana Math MT.CORE.ALG.QUAD.3.b
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: Converting between factored, standard, and vertex forms symbolically and using representations,
2026 Montana Mathematics Content Standards · Algebraic and Functional Reasoning
Teacher's field guide
What This Standard Means
What Students Need to Do
- Students rewrite the same quadratic in factored, standard, and vertex forms. They use a graph to check that the forms describe the same function and to locate zeros, the y-intercept, and the vertex.
What Mastery Looks Like
- Given y=2x²-8x+6, a student writes 2(x-1)(x-3) and 2(x-2)²-2. They identify the zeros as 1 and 3, the y-intercept as 6, and the vertex as (2, -2).
Common Misconceptions
- Students may expand (x-3)² as x²-9 or forget to multiply every term by the leading coefficient. They may read the vertex of (x-2)²-2 as (-2, -2) or mistake the y-intercept for a zero.
How to Assess It
- Exit ticket: Rewrite f(x)=x²-6x+5 in factored and vertex forms. Label its zeros and vertex on a quick sketch.
Lesson moves
Ways to Teach It
Give pairs graph paper and y=(x-1)(x-5); have them plot the zeros, find the vertex, and write vertex form.
Ask students which form of y=2x²-8x+6 shows the y-intercept, zeros, or vertex most clearly, and why.
Have groups match cards showing 2(x-1)(x-3), 2x²-8x+6, 2(x-2)²-2, and a graph, then explain their matches.
Give students the ball-height model h(t)=-(t-2)²+4; have them find the peak, rewrite it in factored form, and find the landing time.
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Related Standards
- MT.PLUS.ALG.POLY.2.b
Converting between factored and standard form symbolically and using representations (e.g., area model), and
- 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.CORE.ALG.QUAD.3.d
Understanding the relationship between vertex form and the vertex of the function.
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