Factors of parabolas1

$$x+10$$

$$x-10$$

$$x-3$$

$$x+3$$

$$x+7$$

$$x+11$$  

$$x-2$$  

$$x-11$$  

$$x+9$$  

$$x+2$$  

The zeros, -6 and 6, can be found when

$$0=\left(x+6\right)\left(x-6\right).$$

The only zero, 6, can be found when

$$0=\left(x-6\right)\left(x-6\right).$$

The only zero, 18, can be found when

$$0=\left(x-18\right)\left(x-18\right).$$

The zeros, -18 and 18, can be found when

$$0=\left(x+18\right)\left(x-18\right).$$

The zeros, -7 and 7, can be found when

$$0=\left(x+7\right)\left(x-7\right).$$

The only zero, 7, can be found when

$$0=\left(x-7\right)\left(x-7\right).$$

The only zero, 24.5, can be found when

$$0=\left(x-24.5\right)\left(x-24.5\right).$$

The zeros, -24.5 and 24.5, can be found when

$$0=\left(x+24.5\right)\left(x-24.5\right).$$

$$4\left(3m-5\right)\left(3m+5\right)$$  

$$\left(9m-20\right)\left(4m+5\right)$$  

$$2\left(2m-5\right)\left(9m+10\right)$$  

$$4\left(3m-5\right)^2$$  

$$4\left(2m-4\right)\left(2m+4\right)$$  

$$\left(8m-32\right)\left(2m-4\right)$$  

$$2\left(2m-8\right)\left(16m+16\right)$$  

$$4\left(4m-8\right)^2$$  

$$x+3$$

$$x-3$$

$$x-9$$

$$x+9$$

$$x+6$$

$$x+7$$  

$$x-2$$  

$$x-7$$  

$$x+5$$  

$$x+2$$  

The zeros, -12 and 12, can be found when

$$0=\left(x+12\right)\left(x-12\right).$$

The only zero, 12, can be found when

$$0=\left(x-12\right)\left(x-12\right).$$

The only zero, 72, can be found when

$$0=\left(x-72\right)\left(x-72\right).$$

The zeros, -36 and 36, can be found when

$$0=\left(x+36\right)\left(x-36\right).$$

$$p\left(x\right)=x^2-25$$  

$$p\left(x\right)=x^2+25$$  

$$p\left(x\right)=x^2+10$$  

$$p\left(x\right)=x^2-10$$