🧱 Shaky on the basics? Start with Foundations →
Maximizing & Minimizing — Visual Lab
Every quadratic has one turning point — the highest or lowest value it can reach. Move the dials, and watch where it lands.
Module 05 · Topic 1 · Quadratic Functions
This is the Parabola Lab. The equation \(y = ax^2 + bx + c\) is on a set of three sliders.
Drag any one and the curve redraws instantly — vertex, axis of symmetry, and roots all follow.
The whole point of Module 5 is finding that turning point and reading what it means, so here you can
see it move before you ever solve for it on paper.
📖 Student Edition for this module (PDF)
The Parabola Lab
Drag a, b, and c. Then switch the form panel between standard, vertex, and factored — all three describe the same curve on the screen.
Parabola Lab. The filled point is the vertex — the maximum if the curve opens down, the minimum if it opens up. The dashed line is the axis of symmetry. The points on the x-axis are the real roots (where \(y = 0\)); when the discriminant \(b^2 - 4ac < 0\) the curve lifts off the axis and there are none.
Make It Make Sense
A quick read on what the lab is showing you, and a few experiments to run.
What you're seeing
- a sets direction and width. Positive opens up (a minimum); negative opens down (a maximum). Bigger \(|a|\) makes a narrower curve.
- c is the y-intercept — the curve always passes through \((0, c)\).
- The vertex sits at \(x = -\tfrac{b}{2a}\); the axis of symmetry is the vertical line through it.
- The roots are where the parabola crosses the x-axis. The discriminant \(b^2 - 4ac\) decides whether there are two, one, or none.
Try this
- Set a = 1, b = 0, c = 0 for the parent \(y = x^2\). Now slide c up and down — the whole curve lifts and drops, vertex and all.
- Make a negative. Watch the min/max banner flip from MINIMUM to MAXIMUM as the parabola turns over.
- Find a quadratic with no real roots (lift it off the x-axis) and confirm the discriminant goes negative.
- Switch to the Factored form and tune the sliders until the two factors show clean whole-number roots.
Key Vocabulary & Standards
The words a mathematician uses for the parts of a parabola — and the TEKS this lab is built to teach.
Parabola
The U-shaped graph of a quadratic function \(y = ax^2 + bx + c\), where \(a \ne 0\).
Vertex
The single turning point — the maximum or minimum value of the function, at \(x = -\tfrac{b}{2a}\).
Axis of Symmetry
The vertical line \(x = -\tfrac{b}{2a}\) that mirrors the parabola onto itself.
Roots / Zeros
The x-values where \(y = 0\) — where the curve meets the x-axis. Also called solutions or x-intercepts.
Discriminant
\(b^2 - 4ac\). Positive → two real roots, zero → one, negative → none.
Three Forms
Standard \(ax^2+bx+c\), vertex \(a(x-h)^2+k\), and factored \(a(x-r_1)(x-r_2)\) — one curve, three views.
A.6 — graphing quadratic functions · A.7 — attributes of parabolas (vertex, axis, roots, direction) · A.8 — solving quadratic equations. RDY marks STAAR readiness standards.