Question

The expressions below model different possibilities for the area of a pool. Identify which of the following expressions have at least the one zero greater than 4.
X^2+11x+30
X^2-5x-14
X^2+5x-24
X^2-5x+6

Answer 1

Answer: Choice B is correct

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Explanation:

Use a graphing tool like GeoGebra, Desmos, or your graphing calculator to plot each expression given as a separate y equation. Four parabolas should result.

The x intercept is the same as the root or zero of a function.

You should find that only choice B has a root thats larger than 4. That specific root being x = 7.

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A non-graphing approach:

You can use the quadratic formula or the factoring method to find the roots.

For choice A, it factors to (x+5)(x+6) = 0. The roots are x = -5 and x = -6 which aren't greater than 4. So we cross choice A off the list. Choices C and D are similar stories.

On the other hand, choice B factors to (x-7)(x+2) = 0 and it has roots of x = 7  and x = -2. This is another way to see why choice B is the answer.

Here are the steps for the quadratic formula for choice B

$x = \frac{-b\pm\sqrt{b^2-4ac}}{2a}\\\\x = \frac{-(-5)\pm\sqrt{(-5)^2-4(1)(-14)}}{2(1)}\\\\x = \frac{5\pm\sqrt{81}}{2}\\\\x = \frac{5\pm9}{2}\\\\x = \frac{5+9}{2} \ \text{ or } \ x = \frac{5-9}{2}\\\\x = \frac{14}{2} \ \text{ or } \ x = \frac{-4}{2}\\\\x = 7 \ \text{ or } \ x = -2$

The quadratic formula is handy in case factoring is either not possible, or guess-and-check is too lengthy of a process. As you can probably tell, we could use the quadratic formula's results to help construct the factored form.