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QUADTRATIC RELATIONS Standard Form

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**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

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**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

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**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)

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**GrAPHING QUADRATICS IN Standard form**

COMPLETE QUESTION 4! Determine the line of symmetry and the coordinates of the vertex for a - f

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**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.

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**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

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**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)

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

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**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

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**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.

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**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

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**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)

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

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**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

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**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

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**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.

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