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