Standard & Vertex Form of Quadratics

Causes shift left and right

Causes shift up and down

Graph opens upward & Stretch/compress

Has no affect on transformation of the graph.

Graph opens downward (reflection)

g(x) = x² - 5

g(x) = x² + 5

g(x) = (x - 5)²

g(x) = (x + 5)²

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

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

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

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

f(x)= 5(x - 2)²

f(x) = 5(x + 2)²

f(x) = (x - 2)² - 5

f(x) = (x + 2)² + 5

opens up with a maximum; y-int = (0, -2)

opens up with a minimum; y-int = (0, 2)

opens down with a maximum; y-int = (0, -2)

opens down with a minimum; y-int = (0, 2) 

(-2,-5)

(-2,5)

(2,-5)

(-5,2)

x-intercepts

zeros

y-intercept

solutions

vertex