Roots and Zeros

STAAR Tips and Tricks for Solutions/Roots/Zeros

Solutions/Roots/Zeros

When a question asks you to find the solution, root, and/or the zero, all three mean the same.

The solutions/roots/zeros are the x-values where the function crosses the x-axis. In this example, the solutions/roots/zeros are -2 and 2. This is the function $f\left(x\right)\ =\ x^2-4$  .

Multiple Choice

What are the approximate zeros for this function?

• -2 and 2

• -1 and 1

• -1.4 and 1.4

• -1.8 and 1.8

Some functions will be in the form of an equation. This is a tip/trick for finding them with Desmos.

• Make sure  $f\left(x\right)$  or  $y$   must be alone on one side of the equation.

• Sometimes the problem will not have either of those, but a  $0$  instead. e.g.  $3x^2-4x-9=0$  

• If this is the case, you will graph the equation as  $y=3x^2-4x-9$  

• If you have an equation with multi-term expressions on both sides, e.g.  $-3x^2+2x=26$  ,you must solve for  $0$  ,  e.g. $-3x^2-2x-26=0$  , and graph it as  $y=-3x^2-2x-26$  .

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What is one of the roots of  $$-4x^2=-2x-7$$  ? Round to the nearest tenths.

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What is one of the solutions of   $$g\left(x\right)=x^2-5x-2$$  ? Round to the nearest tenths.

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What is one of the zeros for   $$-10x^2-12x+9=0$$  ? Round to the nearest tenth.

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What is one of the zeros for  $$5x^2-3y=12$$  ? Round to the nearest tenth.