6.5 Finding AOS and Y Intercept AOS: -b/2a Y Intercept: C.

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6.5 Finding AOS and Y Intercept AOS: -b/2a Y Intercept: C

6.5 Finding AOS and Y Intercept We’ve finished 6.2 and can graph using a table and plotting at least five points. We are going to look for other critical points that we can graph with without using a table. These points are called… AOS: Axis of symmetry (-b/2a) – An imaginary (dotted) line that travels down the middle of a parabola. Y intercept: The point where a line crosses the “Y” axis. Y Intercept AOS

6.5 Finding AOS and Y Intercept Let’s look at a possible homework question: Ex 1: What are the AOS and Y Intercept of this equation 3x 2 + 6x = 7 Step 1: Make the equation = 0 (you must move the 7; how?) 3x 2 + 6x – 7 = 0 Step 2: Find AOS by using this formula -b/2a (Hint: Find A, B, C first) A=3, B=6, C=-7 -b = -6 = -6 = -1 2a 2(3) 6 AOS is -1 A B C Dotted line at x = -1

6.5 Finding AOS and Y Intercept Here are the steps from a different problem… 2x 2 + 5x + 12 = 0 A=2, B=5, C=12 -b = -5 = -5 = a 2(2) 4 AOS is Now for the Y Intercept: The Y intercept occurs when we replace “x” with “0”. Let’s look 2(0) 2 + 5(0) Y Intercept = 12 (Hint: this is just “C” in your equation) A B C Dotted line at x = -1.25

6.5 Finding AOS and Y Intercept OK. So “C” is my Y Intercept. What do we do with it? The Y intercept is somewhere on the Y Axis (vertical line). y x For the equation 2x 2 + 5x + 12 = 0 The Y Int is +12. Put a point here (12) and you are all done!

6.5 Finding AOS and Y Intercept Review before we end… A quadratic equation has A, B, and C You must set the pattern to ax 2 + bx + c = 0 The AOS (Axis of Symmetry) is just –b/2a The Y intercept is just “C” You must show the Y Intercept, the AOS, and the graph on the assignment. Now go and prove you know what you are doing. Be awesome with your Homework!