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Name:____________________________________________ Date:_______ Period:______ Linear/Quadratic Systems Recall: Graphing a linear function Example: Graph the line: y = 2x – 3 In order to graph a line, in y = mx + b form: Step 1: List the slope and y-intercept. Slope: ___________________________ y-intercept: _______________________ Step 2: Graph the y-intercept. Step 3: From the y-intercept, use the slope to plot the other points on the line. Make sure to fill up the entire graph. Step 4: Using a straight-edge connect all of the points together. In order to graph a line, in point/slope form: y - y1 = m(x - x1) Example: 1 Graph the line: 𝑦 − 4 = − 2 𝑥 + 2 Step 1: List the slope and point. Slope: ___________________________ Point: _______________________ Step 2: Graph the point. Step 3: From the point, use the slope to plot the other points on the line. Make sure to fill up the entire graph. Step 4: Using a straight-edge connect all of the points together. To graph a parabola: y = x2 – 4x – 5 Step 1: Find the axis of symmetry using the equation: 𝑥 = −𝑏 2𝑎 Step 2: Plug the quadratic equation in y= in your calculator. Then check your table. The axis of symmetry should be in the middle of your table. Use 3 values less than & 3 values greater than your axis of symmetry to fill in the table. ***If your axis of symmetry is a fraction, use the two numbers that it falls between as your middle numbers. However, make sure to graph your axis of symmetry on your graph.*** Step 3: Plot all of the points from your table on the graph. Connect the points using a curve. To graph a quadratic/linear system: Example: y = x2 - 4x - 2 y=x–2 Step 1: Graph the line. Step 2: On the same set of axes, graph the parabola. Step 3: Write down the points where the line and parabola intersect. Box them in, this is your final answer. What happens if a quadratic/linear system is a Part I question? If a quadratic/linear system is a Part I question, all that we have to do is use our graphing calculator to solve! Let's take a look at the same example: y = x2 - 4x - 2 y=x–2 ***Copy Down the Calculator Steps*** 1) Solve the following quadratic/linear system graphically. y = -x2 + 2x + 4 x+y=4 2) Solve the following system of equations graphically. y = (x – 2)2 + 4 4x + 2y = 14