Graphing Parabolas and Completing the Square

Warm-Up Solve each quadratic below (Hint: When you take the square-root you will get 2 answers; one positive and one negative)

Solve each quadratic below (Hint: When you take the square-root you will get 2 answers; one positive and one negative)

Quadratic Functions Vertex Form If a is positive the parabola opens up. If a is negative the parabola opens down. Remember Transformation Rules: x-h moves right, x+h moves left -k moves down, +k moves up Therefore, Vertex: (h, k)

Use Vertex Form to Sketch a Parabola Step 1: Find a. Does the parabola open up or down? Step 2: Identify the vertex (h, k) Step 3: Set the equation equal to zero and solve for x (these are the zeros or x-intercepts: where the graph will cross the x-axis) Step 4: Sketch the parabola

Example 1: Step 1: a = -3, so the parabola opens down Step 2: The vertex is (-2, -1). (Notice, the h is opposite) Step 3: Solve for y=0 Step 4: Vertex(-2, -1)

Example 2:

Example 3:

Example 4:

Solving Quadratic Equations by Completing the Square

Perfect Square Trinomials l Examples l x 2 + 6x + 9 l x x + 25 l x x + 36

Creating a Perfect Square Trinomial l In the following perfect square trinomial, the constant term is missing. X x + ____ l Find the constant term by squaring half the coefficient of the linear term. l (14/2) 2 X x + 49

Perfect Square Trinomials l Create perfect square trinomials. l x x + ___ l x 2 - 4x + ___ l x 2 + 5x + ___

Solving Quadratic Equations by Completing the Square Solve the following equation by completing the square: Step 1: Move quadratic term, and linear term to left side of the equation, constant term to the right side:

Solving Quadratic Equations by Completing the Square Step 2: Find the term that completes the square on the left side of the equation. Add that term to both sides.

Solving Quadratic Equations by Completing the Square Step 3: Factor the perfect square trinomial on the left side of the equation. Simplify the right side of the equation.

Solving Quadratic Equations by Completing the Square Step 3B: Once you have completed the square you can also write the quadratic in vertex form by simply setting everything equal to zero (subtract 36 from both sides) Vertex Form

Solving Quadratic Equations by Completing the Square Step 4: Take the square root of each side

Solving Quadratic Equations by Completing the Square Step 5: Set up the two possibilities and solve

Solving Quadratic Equations by Completing the Square Try the following examples. Solve by completing the square. Then write in vertex form.

Solve by Completing the Square

Homework Sec 2.4: 20-30, 32-34, 40