5.2 Graphing Quadratic Functions in Vertex Form 12/5/12

Equations of a line… Slope intercept form: y = mx + b Ex: y = 3x + 2 Point – slope form: y - y 1 = m(x – x 1 ) Ex: y – 5 = 3(x – 1) Standard form: Ax + By = C Ex: 3x – 2y = 5

Equations of a Parabola… Standard Form: y = ax 2 + bx + c Ex: y = 2x 2 + 4x + 9 Vertex Form: y = a(x-h) 2 + k

(h, k) is the vertex Vertex Form:a quadratic equation written in the form Y = a(x –h) 2 + k (h, k) Again… When a is positive, the parabola opens up. When a is negative, the parabola opens down. Graphing Method: Follow the same 4 steps as the standard form except vertex can be determined right away in the equation.

Example 1 Graph a Quadratic Function in Vertex Form Graph. ()2)2 2x – y = 2 – 1 + The function is in vertex form where, h 2, and k 1. Because a < 0, the parabola opens down. = a = 2 – y = ak + ()2)2 hx – = STEP 2 Draw the axis of symmetry through the vertex. STEP 1Plot the vertex,. () h, kh, k () 2, 12, 1 = STEP 3Create x-y chart. Pick 2 values for x to the right or left of the line of symmetry. Find the corresponding y.

Example 1 Graph a Quadratic Function in Vertex Form ()2)2 23 – y = 2 – 1 + = 1 – ()2)2 24 – y = 2 – 1 + = 7 – One point on the parabola is. () 3,3, – 1 STEP 4Draw a parabola through the points. Plot the points and. Then plot their mirror images across the axis of symmetry. () 3,3, – 1 () 4,4, – 7 Another point on the parabola is () 4,4, – 7. xy 3 4-7

Checkpoint Graph a Quadratic Function Graph the function. Label the vertex and the axis of symmetry. ANSWER 1. ()2)2 3x – y = 1 –

Checkpoint Graph a Quadratic Function Graph the function. Label the vertex and the axis of symmetry. ANSWER 2. 3 y = ()2)2 2x –– +

Checkpoint Graph a Quadratic Function Graph the function. Label the vertex and the axis of symmetry. ANSWER 3. 4 y = ()2)2 1x 2 ++

Checkpoint Graph a Quadratic Function Graph the function. Label the vertex and the x -intercepts. ANSWER 5. () 3x – y = () 1x + 2

Maximum and Minimum Value of the Quadratic Eqn. Vertex is the highest point, therefore the y-coordinate of the vertex is the maximum value. Vertex is the lowest point, therefore the y-coordinate of the vertex is the minimum value.

Find the Minimum or Maximum Value Tell whether the function has a minimum or maximum value. Then find the minimum or maximum value. ()2)2 8xy = 12 – ANSWER minimum; 12 – Find the vertex: (h, k) is (-8, -12) Since a is positive, the parabola opens up and the vertex is the lowest point. Take y-coordinate as the minimum value of the function.

Homework 5.2 p.231 #22-27 Graph #35-38, 41 #56-58