Quadratic Functions Vertex Form – Notes & Homework

Identify the vertex and line of symmetry of a quadratic function written in vertex form.

Determine whether a quadratic function has a maximum or minimum value from its vertex form.

Predict whether a parabola opens upward or downward and whether it is narrow, normal, or wide based on the leading coefficient a.

Convert a quadratic function from standard form to vertex form by completing the square, as modeled in the guided notes.

Work through the guided notes as a class before assigning the homework, since the homework repeats the same four question types (vertex, line of symmetry, max/min, and graph prediction) with new functions.

Have students complete the a-value table on page 5 before graphing, so they connect the sign and size of a to the parabola's direction and width ahead of sketching.

Because two homework items ask students to sketch a graph from a table rather than fill in a blank, leave room in the lesson for students to draw their own axes.

Vertex identification — students read the vertex (h, k) directly from functions written in vertex form such as f(x) = 2(x - 4)^2 + 6.

Line-of-symmetry and extrema reasoning — students state the line of symmetry x = h and classify each vertex as a maximum or minimum.

Coefficient-to-shape reasoning — students use the value of a in a table to predict whether a parabola opens up or down and whether it is narrow or wide.

Graphing from vertex form — students sketch parabolas by first predicting shape and direction, then building a table of values around the line of symmetry.