How to Graph Quadratic Functions on TI-84 Calculator

A parabola behaves differently from a line in ways that actually matter for how you enter and read it on a TI-84 the shape changes based on coefficients you can predict before you even graph, and the form the equation is written in changes how easy it is to spot the vertex. This guide covers both standard form and vertex form, plus what the numbers in the equation tell you before you press GRAPH at all.

Does this apply to your TI-84?

Yes, TI-84, TI-84 Plus, and TI-84 Plus CE all graph quadratics the same way.

Graphing from standard form (y = ax² + bx + c)

Example: graph y = x² − 4x + 3

1. Press Y=
2. Type X^2-4X+3 — use the ^ key for the exponent
3. Press GRAPH
4. If nothing appears, press ZOOM, then 6: ZStandard

Graphing from vertex form (y = a(x − h)² + k)

Vertex form is worth using when you already know or want to emphasize the vertex, since (h, k) is the vertex directly no calculation needed to find it once graphed.

Example: graph y = 2(x − 3)² + 1 (vertex at (3, 1))

1. Press Y=
2. Type 2(X-3)^2+1 the parentheses around (X-3) are required; without them, the exponent only applies to X, not the whole expression
3. Press GRAPH

This graphs the same type of parabola as standard form it’s the same underlying shape, just written to make the vertex obvious at a glance instead of requiring the CALC menu or the axis of symmetry formula to find it.

What does the leading coefficient (a) tell you before you even graph?

You can predict the parabola’s basic shape from the equation alone, which helps you set a reasonable graph window before hunting for one:

• Sign of a positive means the parabola opens upward (a minimum point); negative means it opens downward (a maximum point)
• Size of |a| a large value (like 5) makes the parabola narrow, rising or falling steeply; a small value (like 0.2) makes it wide and flat

Knowing this in advance helps explain why a parabola might look “too flat” or “too steep” and cut off in the default window — it’s often just a, not a mistake.

How do I find the vertex without switching to vertex form?

If your equation is in standard form and you don’t want to convert it, there are two options:

Axis of symmetry formula the vertex’s x-coordinate is always x = −b/(2a). Calculate this by hand or on the home screen, then substitute it back into the original equation to get the y-coordinate.

CALC menu press 2nd, then TRACE, and select 3: minimum (if the parabola opens up) or 4: maximum (if it opens down). This is covered in full detail, including bound selection, in the dedicated vertex guide.

How do I find the x-intercepts?

Press 2nd, then TRACE, and select 2: zero. Set bounds around each x-intercept individually a parabola typically has up to two, and it’s easy to find one and assume you’re done. If the parabola doesn’t cross the x-axis at all, it has no real x-intercepts, which the graph shape (opening away from the axis entirely) will make visually clear.

Common mistakes and how to fix them

Missing parentheses in vertex form. 2X-3^2+1 is not the same as 2(X-3)^2+1 without the parentheses, the exponent only applies to the 3, breaking the entire shape of the parabola.

Assuming a flat-looking curve is wrong. A small |a| value produces a genuinely wide, flat-looking parabola that’s expected behavior, not a graphing error. Check the coefficient before assuming something’s broken.

Confusing the vertex with an x-intercept. The vertex is the parabola’s turning point; x-intercepts are where it crosses the x-axis. A parabola with no real solutions still has a vertex — the two aren’t dependent on each other.

Forgetting the squared term’s exponent entirely. Leaving out the ^2 turns a parabola into a straight line, which is a common accidental typo, not a calculator issue.

Practice both forms

The TI-84 Calculator Tool on this site graphs both standard and vertex form the same way as the physical calculator useful for comparing how the same parabola looks when written each way.

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