What are roots and zeros? How are they different?

**Functions have zeros and equations have roots. It is important to know that the zeros refer to when the value of x makes the function equal to zero. In other words, \(y=0\).**

**Zeros are where the function intercepts the x-axis.**

1. Find the zeros of the following quadratic functions by factorization, inspection, or the quadratic formula.

a) \(f(x)=x^2+2x+4\)

b) \(f(x)=3x^2-2\)

c) \(f(x)=2x^2+5x+4\)

d)

1). Did you find the following zeros:

a. No zeros , used the quadratic formula or could use the graph, does not cross the \(x\)-axis

b. Zeros are \(x = \frac{\sqrt{2}}{3}\) and \(x=-\frac{\sqrt{2}}{3}\)

c. No zeros , used the quadratic formula or the graph, does not cross the \(x\)-axis

d. x-intercepts or zeros are: \((-6,0),(-3,0)\)

2). What strategies do you use for factoring? Once the function had been factored, how did you find the zeros?

Note: If you are having trouble with factoring quadratics, the POLQ modules review factoring of quadratics.

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