In week 9 of Precalc, we dove into quadratic functions, we learned about the standard form of quadratic functions and this is the formula:

Y=A(X−C)^2+D

the A and D are the x and y of a point, usually introduced in a question, and the X and Y values will be the vertex, also introduced in the same question. The way this formula works is you have to find the A value by replacing ACXY by their given units, then rewrite it as Y=A(X−C)^2+D with the X and Y as the variables X and Y, this is how you graph it.

The way to graph a quadratic function is simple when you know what every unit does.

The A unit is the stretch, it will effect the parabola, making it wider or thinner.

The (X−C)^2 tells you where the vertex will be on the X axis. The way it works is weird because negative actually makes it move up by positive C. this means when you see (X−6)^2 for example, the vertex will be on X6, and so will the axle of symmetry.

The +D will basically move the vertex vertically. whatever D is, is where your vertex is on the Y axis.

Putting it all together, this is what the function Y=3(X-5)^2+2 will look like