Graphing Quadratics in Standard Form

a = 1, b = 0, c = 0

a = 0, b = 1, c = 0

a = 1, b = 1, c = 1

a = 0, b = 0, c = 0

$$f\left(x\right)\ =\ a\left(x\ -\ h\right)^2+k$$  

$$f\left(x\right)\ =\ a\left(x\ -\ r\right)\left(x\ -s\right)$$  

$$x=\ -\frac{b}{2a}$$  

All real numbers

y ≥ 0

y ≤ 0

x ≥ 0

y ≤ 0

$$x\ =\ \frac{6}{2\left(1\right)}$$

$$x\ =\ \frac{2}{6\left(1\right)}$$

$$x\ =\ -\frac{6}{2\left(1\right)}$$

$$x\ =\ \frac{-6}{-2\left(1\right)}$$

$$x\ =\ \frac{1}{6\left(2\right)}$$

-6

-3

3

6

$$-\left(3\right)^2+6\left(-3\right)\ +\ 8$$

$$\left(-3\right)^2+6\left(-3\right)\ +\ 8$$

$$\left(3\right)^2+6\left(3\right)\ +\ 8$$

$$\left(-3\right)^2+6\left(x\right)\ +\ 8$$

$$1$$

$$-1$$

$$0$$

$$3$$

$$\left(-3,\ -1\right)$$

$$\left(3,\ 1\right)$$

$$\left(3,\ -1\right)$$

$$\left(-3,\ 1\right)$$

$$\left(-1,\ -3\right)$$