11. Express 1.132 in the form of 5, where q * 0.

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naenae2cold12021

30.11.2022

Mathematics

You can factor a parabola by finding its roots: if

p(x)=x^2+bx+c

has roots $x_1,\ x_2$ , then you have the following factorization:

p(x) = (x-x_1)(x-x_2)

In order to find the roots, you can use the usual formula

$x_{1,2} = \dfrac{-b\pm\sqrt{b^2-4ac}}{2a}$

In the first example, this formula leads to

$x_{1,2} = \dfrac{-2\pm\sqrt{4+4}}{2} = \dfrac{-2\pm\sqrt{8}}{2} = \dfrac{-2\pm2\sqrt{2}}{2} = 1 \pm \sqrt{2}$

So, you can factor

$x^2-2x-1 = (x-1-\sqrt{2})(x-1+\sqrt{2})$

The same goes for the second parabola.

As for the third exercise, simply plug the values asking

f(1.5)=-5.25

you get

f(-1.5) = 1.5c-3 = -5.25

Add 3 to both sides:

1.5c = -2.25

Divide both sides by 1.5:

c = 1.5

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