1. Graphing Quadratic Equations
a step-by-step guide
with practice

2. Graphing from Standard Form
Graph y = x2 – 6x + 8.

3. Graphing from Standard Form
Graph y = x2 – 6x + 8.
Step 1: Find the axis of symmetry.

4. Graphing from Standard Form
Graph y = x2 – 6x + 8.
Step 2: Find the vertex.
Vertex: (3, – 1)

5. Graphing from Standard Form
Graph y = x2 – 6x + 8.
Step 3: Graph using quadratic pattern.

6. Graphing from Standard Form
Graph y = x2 – 6x + 8.
What are the roots?
(2,0) & (4,0)

7. Graphing from Intercept Form
Graph y = (x – 4)(x + 2).

8. Graphing from Intercept Form
Graph y = (x – 4)(x + 2).
Step 1: Find the x-intercepts.
x – 4 = 0
x = (4,0)
x + 2 = 0
x = – 2 (-2,0)

9. Graphing from Intercept Form
Graph y = (x – 4)(x + 2).
Step 2: Find the axis of symmetry.

10. Graphing from Intercept Form
Graph y = (x – 4)(x + 2).
Step 3: Graph using quadratic pattern.

11. Graphing from Intercept Form
Graph y = (x – 4)(x + 2).
What are the zeros?
(– 2,0) & (4,0)

12. Graphing from Vertex Form
Graph y = 2(x – 1)2 + 3

13. Graphing from Vertex Form
Graph y = 2(x – 1)2 + 3
Step 1: Find the vertex.
vertex: (1, 3)

14. Graphing from Vertex Form
Graph y = 2(x – 1)2 + 3
Step 2: Find the axis of symmetry.

15. Graphing from Vertex Form
Graph y = 2(x – 1)2 + 3
Step 3: Graph using quadratic pattern.

16. Graphing from Vertex Form
Graph y = 2(x – 1)2 + 3
What are the solutions?
There are NO real solutions because the graph doesn’t cross the x-axis….the solutions are actually imaginary/complex!