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Algebra II Quarter 3: Handout #2 Name ________________________ Date _____________ Period _____ 5.5 Completing the Square (Part 2 - Parabolas) In this lesson we will apply the concept of “Completing the square” to parabolas. This method will give information on the maximums and minimums. What part of an equation tells us we will have a parabola when graphed? What shape is a parabola? What is the difference between a parabola that opens up and a parabola that opens down? Draw and label a diagram! What is the vertex of a parabola? What is the line of symmetry of a parabola? Draw and label a diagram! Memorize!!! The general formula of a parabola is: y = (x – h)2 – k The vertex is given by coordinates: (h, k) The line of symmetry is given by the vertical equation: x = h When you have x2 (positive,) the parabola opens upward and you have a minimum. When you have –x2 (negative,) the parabola opens downward and you have a maximum. Algebra II Quarter 3: Handout #2 Example 1: Write the quadratic function in vertex form. y = x2 – 8x + 11 What is the vertex? ___________________________ What is the line of symmetry? _________________________ Will there be a max or min? Why? __________________________________ Draw and label simple picture: Algebra II Quarter 3: Handout #2 Example 2: Write the quadratic function in vertex form. y = x2 + 12x What is the vertex? ___________________________ What is the line of symmetry? _________________________ Will there be a max or min? Why? __________________________________ Draw and label simple picture: Algebra II Quarter 3: Handout #2 Example 3: Write the quadratic function in vertex form. y = -x2 + 14x - 45 What is the vertex? ___________________________ What is the line of symmetry? _________________________ Will there be a max or min? Why? __________________________________ Draw and label simple picture: Algebra II Quarter 3: Handout #2 Example 4: Write the quadratic function in vertex form. y = 2x2 + 4x - 4 What is the vertex? ___________________________ What is the line of symmetry? _________________________ Will there be a max or min? Why? __________________________________ Draw and label simple picture: Algebra II Quarter 3: Handout #2 Example 5: Write the quadratic function in vertex form. y = x2 + 10x + 17 What is the vertex? ___________________________ What is the line of symmetry? _________________________ Will there be a max or min? Why? __________________________________ Draw and label simple picture: