Write a quadratic function f whose only zero is 7

1 answer:

5 0

well, we know is a quadratic, namely of degree 2, so it has two solutions and namely two factors, and whose only zero is 7, well, we can do that by giving that only zero a multiplicity of 2, so we get two of the same zero.

$\begin{cases} x=7\implies &x-7=0\\ x=7\implies &x-7=0 \end{cases}\qquad \implies \qquad \begin{array}{llll} \stackrel{\textit{multiplicity of 2}}{(x-7)(x-7)}=\stackrel{0}{y} \\\\\\ x^2-14x+49=y \end{array}$

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Step-by-step explanation:

Asuming the described situation is as shown in the figure below, we need to find the distance $h$ between the kite and Jacks house, but first we need to find the $x$ , $y$ and then $d$ .

How?

We will use trigonometry, especifically the trigonometric functions sine and cosine:

For $y$ :

$sin(65 \°)=\frac{y}{45 ft}$ (1)

Where $y$ is the opposite side to the angle and $45 ft$ the hypotenuse.

Isolating $y$ :

$y=40.78 ft$ (2)

For $x$ :

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Where $x$ is the adjacent side to the angle.

Isolating $x$ :

$y=19.017 ft$ (4)

Finding $d$ :

$d=x+100 ft$ (5)

$d=19.017 ft +100 ft$

$d=119.017 ft$ (6)

Now that we have found these values, we have to work with a bigger triangle, where the hypotenuse is the distance between the kite and Jack's house $h$ and the sides are the values calculated in (4) and (6).

So, in this case we will use the <u>Pithagorean theorem</u>:

$h^{2}=y^{2} +d^{2}$ (7)