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**Calculator Shortcut – Solving Trinomials**

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**x2 + 5x + 4 = 0 Solving Trinomials Example 1: Solve for x:**

We can solve for x when there’s an equal sign When x is squared, there will be two numbers that work for this equation

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**x2 + 5x + 4 = 0 Solving Trinomials Example 1: Solve for x:**

There are different things they will ask for: Solve Find the roots Find the solutions Find the zeros

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**x2 + 5x + 4 = 0 Solving Trinomials**

To solve this we can factor it, or we can use our calculators! Let’s see how to use our calculators to solve any trinomial!

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Solving Trinomials Go to y= Enter the equation into Y1 Enter 0 in Y2

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Solving Trinomials Press GRAPH You should see the graph on your screen

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**Solving Trinomials Press 2nd CALC Go to 5: INTERSECT and press enter**

You should be back at the graph

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Solving Trinomials Move your cursor to where the equation crosses the x-axis on the right side Press ENTER Keep the cursor where it is and press ENTER again

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**Solving Trinomials It should now be asking you to Guess**

Press ENTER one more time The X value is one of your two answers!

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Solving Trinomials We have to follow the same steps to find the other answer Press 2nd CALC Go to 5: INTERSECT and press enter You should be back at the graph

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Solving Trinomials Move your cursor to where the equation crosses the x-axis on the left side Press ENTER Keep the cursor where it is and press ENTER again

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**Solving Trinomials It should now be asking you to Guess**

Press ENTER one more time The X value is your second answer

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**x2 + 5x + 4 = 0 Solving Trinomials Example 1: Solve for x:**

The answer to this are the two x-values you found: -1 and -4

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**Solving Trinomials This technique works anytime there’s an x2 value!**

Always make sure all the numbers are on one side of the equals sign and zero is on the other!

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**x2 + x = 6 -6 -6 x2 + x – 6 = 0 Solving Trinomials**

Example 2: Find the roots of x2 + x = 6 You have to get all the numbers on one side of the equals, so subtract 6 from both sides x2 + x – 6 = 0

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**x2 + x – 6 = 0 Solving Trinomials**

Now plug the equation into y1 and zero for y2 x2 + x – 6 = 0

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**-2x2 + x – 5 = 0 Solving Trinomials Example 3: Find the solutions to**

When you graph this you should see: If it doesn’t cross the x- axis then there’s no solution

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