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