Solving Quadratic Equations Graphically
Given the function $\displaystyle {f{{\left({x}\right)}}}={x}^{{2}}-{4}{x}-{6}$ find x when $\displaystyle {f{{\left({x}\right)}}}=-{10}$ using your graphing calculator. Then follow the steps below to show the intersection graph on the computer. [Hint: Use the following window on your graphing calculator: Xmin = -5, Xmax = 7, Ymin = -15, Ymax = 5] Write the points of intersection as a list of ordered pairs below. Round the values of $\displaystyle {x}$ to two decimal places. [Hint: If two solutions exist, enter them as $\displaystyle {\left({x}_{{1}},{y}_{{1}}\right)},{\left({x}_{{2}},{y}_{{2}}\right)}$. If only one exists, enter $\displaystyle {\left({x}_{{1}},{y}_{{1}}\right)}$. If none exist, enter $\displaystyle {D}{N}{E}$] Use the Line Tool to draw the Horizontal Line $\displaystyle {y}=-{10}$. Use the Polynomial Tool to draw $\displaystyle {f{{\left({x}\right)}}}={x}^{{2}}-{4}{x}-{6}$. [Hint: You will need to find the vertex and one other point] Use the Point Tool to identify the points of intersection.
Write the Points of Intersections as a list of Ordered Pairs
Draw the resulting graph and plot the points of intersection Clear All Draw:

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