February 1, 2012 At the end of today, you will be able to find the solutions/roots/zeros/x-intercepts of a quadratic function by graphing. Warm-up: Identify.

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February 1, 2012 At the end of today, you will be able to find the solutions/roots/zeros/x-intercepts of a quadratic function by graphing. Warm-up: Identify the axis of symmetry, vertex, and y-intercept of the quadratic function below. Axis of sym: x = -2 Vertex: max (-2, 4) y-int: (0, 0) x-intercepts = solutions = roots = zeros (-4, 0) and (0, 0)

Check HW 6.2 Pg. 291 # x = 40; (40, 40) m ft; 2.5 sec 47. The y-intercept is the initial height.

Lesson 6.2 Solving Quadratics by Graphing 3 possible solution scenarios If your graph looks like this… You will have… 2 Real Solutions 1 Real Solution No Real Solutions

Look at CW 6.1, Find the solutions/zeros/roots for each quadratic function. 1. y = x 2 + 6x y = -x 2 – 4 3. y = -x 2 – 4x – 3 4. y = x 2 – 6x y = 3x 2 6. y = 2x 2 + 6x + 4 (-5, 0) (-1, 0) No real roots (-3, 0) (-1, 0) No real roots (0, 0) (1, 0) (2, 0)

When we are solving a quadratic… y is ALWAYS equal to zero! The x-intercepts are the “solutions”. The x-intercepts are the “roots”. The x-intercepts are the “zeros”.

Do one on your own… Solve the quadratic equation by graphing. *Find the axis of sym, vertex, and left/right points. x 2 + 6x + 8 = 0 x y vertex:

How to check your solutions on your calculator… First way: First type in the function in “Y = “ Go to 2 nd -- > Graph - Check that your table is the same as the calculators Second way: First type in the function in Y = Go to Graph - Make sure you can see the entire graph on your window. 2 nd -- > Trace -- >Select #2 zero Left bound? Move your cursor to the “left” of the x-int, then press enter. Right bound? Move your cursor to the right of the xint, then press enter. Guess? Press enter again.