quadtratic relations standard form. graphing quadratics in standard form step 1: determine the line...

QUADTRATIC RELATIONS

Standard Form

GRAPHING QUADRATICS IN STANDARD FORM

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

y= ax2 + bx + c

GRAPHING QUADRATICS IN STANDARD FORM

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

y= ax2 + bx + c

x=−b2 a

x=−(−2)2(4)

x=28 x=0.25

GRAPHING QUADRATICS IN STANDARD FORM

B. To find the y value of the vertex, substitute this into the equation.

y= 4x2 – 2x + 5

x=0.25

At x=0.25, y= 4(0.25)2 – 2(0.25) + 5 = 0.5 - 0.5 + 5 =5

∴, the coordinates of the vertex are (0.25, 5)

GRAPHING QUADRATICS IN STANDARD FORM

COMPLETE QUESTION 4!Determine the line of

symmetry and the coordinates of the

vertex for a - f

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.

GRAPHING QUADRATICS IN STANDARD FORM1) Find the Line of Symmetry

y= 3x2 - 6x + 5

Identify the variables

a=3, b=-6, c=5

Substitute into the formula:

y= ax2 + bx + c

x=−b2 a

x=−(−6)2(3)

x=66 x=1

GRAPHING QUADRATICS IN STANDARD FORM2) 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)

y= 3x2 - 6x + 5

(1, 2)

y= 3x2 - 6x + 53) Graph the vertex

4. USE A TABLE OF VALUES TO DETERMINE POINTS NEAR VERTEX

X y

-1 13

0 4

1 1

2 4

3 13

Use a table of values with x=1,2,3 and x=0,-1 to find more points close to the vertex.

y= 3x2 - 6x + 5

=3(-1)2 - 6(-1) + 5

=13

y= 3x2 - 6x + 5

=3(0)2 - 6(0) + 5

=4

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.

GRAPHING QUADRATICS IN STANDARD FORM1) Find the Line of Symmetry

y= -2x2 + 8x - 3

Identify the variables

a=-2, b=8, c=-3

Substitute into the formula:

y= ax2 + bx + c

x=−b2 a

x=−(8)2(−2)

x=−8−4 x=2

GRAPHING QUADRATICS IN STANDARD FORM2) Find the Coordinates of the Vertex

At x=1, -2(2)2 + 8(2) - 3

=-8+16-3

=5

∴, the coordinates of the vertex are (2, 5)

y=-2x2 + 8x - 3

(2, 5)

y=-2x2 + 8x - 33) Graph the vertex

4. USE A TABLE OF VALUES TO DETERMINE POINTS NEAR VERTEX

X y

0 -3

1 3

2 5

3 3

4 -3

Use a table of values with x=2,3,4 and x=1,0 to find more points close to the vertex.

y=-2(2)2 + 8(2) - 3

=-8+16-3

=5

(0, -3)

(1, 3)

(2, 5)

(3, 3)

(4, -5)

y=-2x2 + 8x - 3

5) Plot & connect the points, arrows and label

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 vertex3) Graph the vertex4) Use a table of values to determine points near the vertex.