Montana Math MT.CORE.ALG.QUAD.3.d
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 vertex form and the vertex of the function.
2026 Montana Mathematics Content Standards · Algebraic and Functional Reasoning
Teacher's field guide
What This Standard Means
What Students Need to Do
- Students read the vertex from an equation in vertex form. They use that point to sketch the graph and tell whether it has a maximum or minimum.
What Mastery Looks Like
- Given y = -2(x + 3)^2 + 8, a student identifies (-3, 8) as the vertex and a maximum. Given a vertex of (4, -1) and a value of 3 for a, they write y = 3(x - 4)^2 - 1.
Common Misconceptions
- Students often say the vertex of y = (x + 3)^2 + 8 is (3, 8), missing the opposite sign inside the parentheses. Some think changing a moves the vertex, rather than changing the graph's shape or direction.
How to Assess It
- Write y = -2(x + 3)^2 + 8 on the board. Ask students to name the vertex, tell whether it is a maximum or minimum, and explain the x-coordinate's sign.
Lesson moves
Ways to Teach It
Have students place sticky dots at x-values from 0 to 4 for y = (x - 2)^2 + 1, then mark the vertex.
Ask: Why do y = (x - 3)^2 + 2 and y = (x + 3)^2 + 2 have vertices on opposite sides of the y-axis?
Play a card match with six vertex-form equations and six vertex coordinates, then check each match by graphing.
Use h = -2(t - 3)^2 + 18 for a thrown ball, and ask when it reaches its greatest height and what that height is.
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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.CORE.ALG.QUAD.3.b
Converting between factored, standard, and vertex forms symbolically and using representations,
- MT.CORE.ALG.QUAD.3.c
Understanding the relationship between factored form and the zeros of the function, and
- MT.CORE.ALG.LIN.4.e
Understanding the relationship between standard form and the x- and y-intercepts.
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