Math 1 Strand
Build confidence with parabolas, factoring, graph features, and real-world quadratic models.
Quadratics connect algebra to visible graph features. Students become stronger when they can choose the form that reveals what the question asks for: zeros, vertex, intercepts, maximums, or minimums.
Use the form that gives you the feature. y = ax^2 + bx + c shows the y-intercept, y = a(x - r)(x - s) shows zeros, and y = a(x - h)^2 + k shows the vertex.
Standards-Aligned Overview
Based on the Math 1 standards for quadratic expressions, equations, functions, and model interpretation.
Choose and produce equivalent forms of quadratic expressions to reveal useful features.
Use zeros and factors to connect algebraic expressions with graph behavior.
Solve quadratic equations using structure, including factoring and square-root reasoning.
Graph quadratic functions and identify key features from the graph or equation.
Use equivalent forms to reveal zeros, extreme values, and symmetry.
Key Vocabulary
These terms support table, graph, equation, and context questions.
A function whose highest power of x is x^2. Its graph is a parabola.
The U-shaped graph of a quadratic function. It can open upward or downward.
The turning point of a parabola. It gives the maximum or minimum value.
The vertical line through the vertex that splits the parabola into matching halves.
Points where the graph crosses the x-axis. They happen when y = 0.
The x-values that make the function equal 0. Zeros match the x-intercepts.
A quadratic written as y = ax^2 + bx + c.
A quadratic written as y = a(x - r)(x - s), which helps reveal zeros.
A quadratic written as y = a(x - h)^2 + k, which helps reveal the vertex (h, k).
The differences of the first differences in a table. Constant second differences suggest a quadratic.
The greatest output value of a downward-opening parabola.
The least output value of an upward-opening parabola.
Student-Friendly Review
Keep the target feature in mind before you start calculating.
Equal first differences mean linear. Equal second differences mean quadratic.
In y = (x - 2)(x + 5), the zeros are x = 2 and x = -5.
In y = a(x - h)^2 + k, the vertex is (h, k).
Zeros can mean when something starts or lands. The vertex can mean the greatest height, greatest profit, or least cost.
Practice Questions
Start with DOK 1 fluency, then build toward applications, analysis, and EOC-style mixed practice.
Practice Set 1
Patterns, forms, zeros, vertex, and intercepts
Practice Set 2
Feature interpretation, factoring, and contexts
Practice Set 3
Justify model choices and critique reasoning
Practice Set 4
Factoring, solving, tables, and graph features
Practice Set 5
Deeper representation switching and modeling
Practice Set 6
A compact EOC-style readiness check