Graphing Quadratics Functions by Completing the Square
Step 1. Put the equation in y=a(x-h)2+k form
a. Group the first two terms of y=ax2+bx+c in parentheses.y=(ax2+box)+c
b. If a is not '1', factor out the coefficient of a.
c. Complete the square by adding (b/2)2. Balance the equation by adding a*(b/2)2 to the left side.
d. Factor the perfect square trinomial on the right into the form (...........)2.
e. Get y by itself.
Step 2. Identify a and (h,k).
Step 3. Graph the "mother points" of y=x2 {(-2,4),(-1,1), (0,0), (1,1), (2,4)}.
Step 4. Multiply the y-values of the "mother points" by a and regraph the points.
Step 5. Translate the graph by sliding it (h,k). units to its new position.
Directions: Please graph the following quadratic function using the form y=a(x-h)2+k.
Step 1. Put the equation in y=a(x-h)2+k form.
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a. Group the first two terms of y=ax2+bx+c in parentheses.y=(ax2+bx)+c |
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b. If a is not '1', factor out the coefficient of a. |
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c. Complete the square by adding (b/2)2. Balance the equation by adding a*(b/2)2 to the left side. |
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d. Factor the perfect square trinomial on the right into the form (......)2. |
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e. Get y by itself. |
Step 2. Identify a and (h,k).
a=2 & (h,k)=(3,-8)
Step 3. Graph the "mother points" of y=x2 {(-2,4),(-1,1), (0,0), (1,1), (2,4)}.
Step 4. Multiply the y-values of the mother points by a and regraph the points.
Step 5. Translate the graph by sliding the vertex (h,k) units to its new position.
Directions: Please graph the following quadratic function using the form y=a(x-h)2+k. Click here for graph paper.
| 1. y=x2-6x+11 | 2. y=2x2-16x+33 | 3. y=3x2+12x+7 |
| 4. y=4x2-5 | 5. y=-3x2-12x-8 | 6. y=3x2-30x+75 |
| 7. y=-4x2-24x-28 | 8. y=-x2+10x-29 | 9. y=1/2x2+2x-1 |