Different forms of quadratics

Grade 10s are working hard to determine the key features of parabolas from different equation forms, and vice versa. We looked at working backwards to create equations given different graph features.

We used symmetry to determine one zero when we knew one zero and the vertex

We worked through all the forms, starting with creating the vertex form equation. We substituted the values of the vertex, and then the given root, we subbed in for x and y. We calculated “a”.

The next form was factored form, so we needed both zeros and a point (the vertex) and we subbed in our values and calculated “a” (which was the same as before! We noticed “a” is the same in all forms).

We expanded to get standard form, and saw the y intercept, the “c” value

By plotting this equation on desmos, we could verify that the vertex and roots were what they were supposed to be.

It’s pretty elegant how all of these forms fit together!