Parabolas - Vertex/standard

Opens up, shifts to the right 5, and shifts up 3

Is narrow, shifts left 5 and up 3

Shifts right 5 and down 3

Opens down and shifts up 3

$$f\left(x\right)=\left(x-1\right)^2-3$$

$$f\left(x\right)=\left(x+3\right)^2-1$$

$$f\left(x\right)=-\left(x-3\right)^2+1$$

$$f\left(x\right)=\left(x-3\right)^2-1$$

$$y=-4x^2+3$$  

$$y=0.2x^2+3$$  

$$y=x^2+3$$  

$$y=4x^2-3$$  

$$f\left(x\right)=-3x^2$$  

$$f\left(x\right)=\frac{1}{3}x^2-1$$  

$$f\left(x\right)=\frac{1}{3}\left(x-1\right)^2$$  

$$f\left(x\right)=3\left(x-1\right)^2$$  

y = 2x² - 12x + 5

y = 2x² - 12x + 23

y = 2x² - 6x + 5

y = 2x² - 12x + 3

y = 3x² - 24x - 41

y = -3x² - 24x - 41

y = -3x² + 24x - 41

y = -3x² - 24x + 41

y = 5x² + 30x - 43

y = 5x² + 30x + 2

y = 5x² + 30x + 43

y = 5x² + 30x - 2

(5, -7)

(-2, -7)

(2, -7)

(-7, -2)

y = 9x² - 15x + 21

y = -3x² - 75x - 4

y = 9x² + 90x + 221

y = -3x² - 30x - 79

$$y=-\frac{2}{3}x^2-12x-52$$  

$$y=-\frac{2}{3}x^2+12x-56$$  

$$y=-\frac{2}{3}x^2+18x-56$$  

$$y=-\frac{2}{3}x^2-18x+52$$  

Compress by 2, shifted 2 units left and 5 down

Stretch by 5, shifted 5 units left and 2 down

Stretch by 2, shifted 2 units left and 5 down

Compress by 5, shifted 2 units left and 2 down

Compress by 2, shifted 2 units left and 5 down

Stretch by 5, shifted 5 units left and 2 down

Stretch by 2, shifted 2 units left and 5 down

Compress by 5, shifted 2 units left and 2 down