4.2 Standard Form of a Quadratic Function Algebra II w/ trig 4.2 Standard Form of a Quadratic Function

Graphing Calculator What are the vertex, the axis of symmetry, the maximum or minimum value, and the range of y = 2x² + 8x – 2?

Quadratic Function: I. Standard Form Equation: y=ax2 + bx + c A. If a > 0, parabola opens upward If a < 0, parabola opens downward B. The axis of symmetry is the vertical line x= C. The x-coordinate of the vertex is at   The y-coordinate of the vertex, is the y value of the function for x= , or y = f( ).   D. The y- intercept is (0,c).

II. Graphing a quadratic function. Step 1. Identify a, b, and c. Step 2. Lightly sketch the axis of symmetry. Step 3. Determine the vertex, then plot it. Step 4. Plot the y intercept (0, 3) and the reflection across the axis of symmetry. Step 5. Draw a smooth curve through the point plotted in steps 3 and 4.

Examples: A. y=2x2-8x+6

Graph B. C. y = ½ x² -3x -2

III. Converting Standard form to Vertex Form Identify a, and b III. Converting Standard form to Vertex Form Identify a, and b. Find the vertex. Then substitute the a term and (h,k), into the vertex form. A. y = 2x² + 10x + 7

B. y = ½ x² - 2x + 5

IV. Interpreting a Quadratic Graph The New River George Bridge in West Virginia is the world’s largest steel single arch bridge. You can model the arch with the function y = -0.000498x² +0.847x, where x and y are in feet. How high above the river is the arch if the base of the parabola formed is 516ft from the river? How long is the section of bridge above the arch?

Pre-Ap Homework p. 206 #9-47 odd