Describe a math problem and get an interactive graph?

Describe a math problem in ordinary English. GoodMaith builds the objects on a live board in the same chat. Drag a point, and whatever depends on it updates. The next sentence can change the figure.

Desmos and GeoGebra are boards where you type the expression and watch. You already know the row to write, or you look up the syntax, and the curve appears because that row is right. Here the sentence comes first. The tutor turns it into points, curves, and labels on the GoodMaith board, beside the words that asked for them.

One sentence, then the figure

You might write: draw $y=x^2-4x+3$, mark the two cuts on the horizontal axis and the vertex, then shift the parabola right by 3.

The first expression factors as $(x-1)(x-3)$, so the arms meet the horizontal axis at $1$ and at $3$. The vertex sits halfway between those cuts. Completing the square writes the same polynomial as $(x-2{)}^2-1$, so the lowest point is $(2,-1)$. On the board those are A, B, and V. The second curve is that parabola moved right by $3$. A point that used to sit at horizontal position $x$ now sits at $x+3$, and the height is unchanged, so the new cuts are $4$ and $6$ and the new vertex W is $(5,-1)$. In completed-square form the shifted curve is $(x-5{)}^2-1$. Both curves stay up together. The shift is something you can point at on one figure, rather than a second drawing on a later slide.

P is a free point on the first curve. Drag it. It has to stay on $y=x^2-4x+3$, so the height you read off is the value of that polynomial. At the left edge of the window, P starts at $(0,3)$, and $0^2-4\cdot 0+3$ is $3$. Move P to the right and the height falls through A, bottoms at V, and rises through B. A, B, and V do not travel with P. They were built as the cuts and the vertex, and they stay put. That is the check that the figure is a construction. A picture of the same parabola would move the whole drawing, labels included, or it would not move at all.

The next sentence

The same chat takes another sentence. "Shift it right by 3" is how the second curve got onto this board. You can keep going in that chat. "Hide the first curve" leaves the shifted one. "Mark the new vertex" is W, already at $(5,-1)$. "What is the height of the new curve at $x=0$?" uses $(x-5{)}^2-1$. At $x=0$ that height is $25-1=24$. Ask for the point and the tutor can put $(0,24)$ on the same board. The window may need to grow to show it. Saying so is another sentence, and the board can follow that sentence too.

One pass through the chat asks a single question and waits. The other writes the path through and plots each object as the reasoning names it. Either way the figure stays the one beside the sentences. You drag it while the explanation is still open.

A geometry sentence uses the same habit. "Draw a circle through three points" builds the circle that has to pass through them. Move one point and the circle still goes through all three. The steps of that construction, and a triangle given two sides and the included angle, are on say the construction and get a draggable figure.

What else the same board can take

When the problem is a solid or a surface, open 3D Graphics on the same board. A plane figure stays on the plane view. The chat does not start over because the picture needs a third axis.

Paste a figure, or upload a photo of the problem. The tutor reads it and builds a construction you can drag. The paste is the input. The thing you drag is the construction made from it, with points that still depend on each other.

You can try the tutor with no account. Sign in when you want those chats kept. The graphing workbench is the board with no tutor, and it stays open without an account. There you type the algebra yourself. The handbook entry on quadratic functions is where the vertex formula and the count of axis cuts are written out, next to figures you can drag.

This page is one worked problem. The product is an AI math solver with live graphs. To start from a sentence of your own, chat with a live board.