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.