Transforming Parabolas

(-2,5)

(2,5)

(5,-2)

(-5,-2)

$$f\left(x\right)=-\left(x+3\right)^2-5$$

$$f\left(x\right)=\left(x-3\right)^2-5$$

$$f\left(x\right)=\left(x+3\right)^2-5$$

$$f\left(x\right)=\left(x+5\right)^2-3$$

(2,-5)

(-5,6)

(2,6)

(5,6)

$$f\left(x\right)=-\left(x-3\right)^2+4$$

$$f\left(x\right)=\left(x-4\right)^2+3$$

$$f\left(x\right)=\left(x-3\right)^2+4$$

$$f\left(x\right)=-\left(x-4\right)^2+3$$

6

4

up

2

1

3

5

down

left

right

y = -(x + 4)² + 2

y = (x + 4)² - 2

y = (x - 4)² - 2

y = (x + 4)² + 2

$$f\left(x\right)=\left(x-3\right)^2+4$$ ; neither even nor odd function

$$f\left(x\right)=-\left(x-3\right)^2+4$$ ; even function

$$f\left(x\right)=-\left(x+3\right)^2+4$$  

neither even nor odd function

even function

odd function

down

up

left

right

y = (x + 5)²

y = (x - 5)²

y = x² - 5

y = x² + 5

$$f\left(x\right)=\left(x-3\right)^2+4$$ ; neither even nor odd function

$$f\left(x\right)=-\left(x-3\right)^2+4$$ ; even function

$$f\left(x\right)=-\left(x+3\right)^2+4$$  

neither even nor odd function

even function

odd function