1. QUADTRATIC RELATIONS
Standard Form

2. GrAPHING QUADRATICS IN Standard form
y= ax2 + bx + c
Step 1: determine the line of symmetry and the vertex
This is a little more difficult since you now have the term bx.
A. To find the line of symmetry, you use the formula:
B. To find the y value of the vertex, substitute this into the equation.
y= ax2 + bx + c

3. GrAPHING QUADRATICS IN Standard form
y= ax2 + bx + c
B. To find the y value of the vertex, substitute this into the equation.
Example: Determine the line of symmetry and the coordinates of the vertex.
y= 4x2 – 2x + 5
Line of symmetry:
a=4, b=-2, c=5
x= −b 2a
x= −(−2) 2(4)
x= 2 8
x=0.25

4. GrAPHING QUADRATICS IN Standard form
y= 4x2 – 2x + 5
B. To find the y value of the vertex, substitute this into the equation.
x=0.25
At x=0.25, y= 4(0.25)2 – 2(0.25) + 5 = =5
∴, the coordinates of the vertex are (0.25, 5)

5. GrAPHING QUADRATICS IN Standard form
COMPLETE QUESTION 4! Determine the line of symmetry and the coordinates of the vertex for a - f

6. Steps for graphing quadratic equations in standard form:
Step 1: determine the line of symmetry
Step 2: Calculate the y coordinates of the vertex
Step 3: draw x, y grid, label the x and y axis, and then plot the vertex
Step 4: Now use a table of values to determine points near the vertex (2 numbers before and 2 numbers after the line of symmetry)
Step 5: Plot the points from your table of values and join them with a curved line. Add arrows to each end and label the graph with the equation.

7. GrAPHING QUADRATICS IN Standard form
y= ax2 + bx + c
1) Find the Line of Symmetry y= 3x2 - 6x + 5 Identify the variables a=3, b=-6, c=5 Substitute into the formula:
x= −b 2a
x= −(−6) 2(3)
x= 6 6
x=1

8. GrAPHING QUADRATICS IN Standard form
y= 3x2 - 6x + 5
2) Find the Coordinates of the Vertex
At x=1, y= 3(1)2 - 6(1) + 5
=3 – 6 +5 =2
∴, the coordinates of the vertex are (1, 2)

9. 3) Graph the vertex
y= 3x2 - 6x + 5
(1, 2)

10. 4. Use a table of values to determine points near vertex
Use a table of values with x=1,2,3 and x=0,-1 to find more points close to the vertex. X y -1 13 4 1 2 3
y= 3x2 - 6x + 5
=3(-1)2 - 6(-1) + 5
=13
y= 3x2 - 6x + 5
=3(0)2 - 6(0) + 5 =4

11. Steps for graphing quadratic equations in standard form:
Step 1: determine the line of symmetry
Step 2: Calculate the y coordinates of the vertex
Step 3: draw x, y grid, label the x and y axis, and then plot the vertex
Step 4: Now use a table of values to determine points near the vertex (2 numbers before and 2 numbers after the line of symmetry)
Step 5: Plot the points from your table of values and join them with a curved line. Add arrows to each end and label the graph with the equation.

12. GrAPHING QUADRATICS IN Standard form
y= ax2 + bx + c
1) Find the Line of Symmetry y= -2x2 + 8x - 3 Identify the variables a=-2, b=8, c=-3 Substitute into the formula:
x= −b 2a
x= −(8) 2(−2)
x= −8 −4
x=2

13. GrAPHING QUADRATICS IN Standard form
y=-2x2 + 8x - 3
2) Find the Coordinates of the Vertex
At x=1, -2(2)2 + 8(2) - 3 = =5
∴, the coordinates of the vertex are (2, 5)

14. 3) Graph the vertex
y=-2x2 + 8x - 3
(2, 5)

15. 4. Use a table of values to determine points near vertex
Use a table of values with x=2,3,4 and x=1,0 to find more points close to the vertex. X y -3 1 3 2 5 4
y=-2(2)2 + 8(2) - 3 = =5

16. 5) Plot & connect the points, arrows and label
(0, -3)
y=-2x2 + 8x - 3
(1, 3)
(2, 5)
(3, 3)
(4, -5)
5) Plot & connect the points, arrows and label

17. GrAPHING QUADRATICS IN Standard form
COMPLETE QUESTION 5! Graph a-h quadratic relations using:
1) Find the line of symmetry
2) Calculate the y coordinates of the vertex
3) Graph the vertex
4) Use a table of values to determine points near the vertex.