This week in Precalculus 11, we learned about equivalent forms of a quadratic function.

**quadratic function:**

**x-intercept: **point on a graph crossing the x-axis

**root: **x-value to an equation when solved

**y-intercept: **point on a graph crossing the y-axis

**vertex: **maximum (opening down) or minimum (opening up) point on a parabola

A quadratic function has 3 forms: factored, general, and standard.

**factored form: **y = a(x – )(x – )

- & are the graph’s x-intercepts, or the equation’s roots

**general form: **y = a + bx + c

- c is the graph’s y-intercept

**standard form: **y = a + q

- p is the vertex’s x-value
- q is the vertex’s y-value

For all 3 forms, a determines whether the parabola opens up (positive) or down (negative) and its stretch (a>1) or compression (a<1) value.

By converting from one form to another, we can determine all elements of the equation.