Using the completing-the-square method, rewrite f(x) = x2 - 6x + 2 in vertex form.

Mathematics

1 answer:

sp2606 [1]3 years ago

8 0

Answer:

$\large\boxed{f(x)+(x-3)^2-7}$

Step-by-step explanation:

$\text{The vertex form of equation}\ y=ax^2+bx+c:\\\\y=a(x-h)^2+k\\\\\text{We have the equation:}\\\\f(x)=x^2-6x+2=x^2-2(x)(3)+1=x^2-2(x)(3)+3^2-3^2+2\\\\\text{Use}\ (a-b)^2=a^2-2ab+b^2\to x^2-2(x)(3)+3^2=(x-3)^2\\\\f(x)=(x-3)^2-9+2=(x-3)^2-7$

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The venticles of a right angle are a[0,4], b[3,-2] c[-3, -4] Find It's area.

givi [52]

Answer:

The area of this triangle is about 21.2132 square units.

Step-by-step explanation:

First, find the lengths of the legs AB and BC.

Length of AB ===

Find the difference in position vertically:

$-2-4=-6$

The points are 6 units apart vertically.

Find the difference in position horizontally:

$3-0=3$

The points are 3 units apart horizontally.

These lengths form a right triangle with the distance between the points as the hypotenuse, so you can use the pythagorean theorem to solve:

$a^2+b^2=c^2\\3^2+6^2=c^2\\9+36=c^2\\45=c^2\\c\approx6.7082$

AB is about 6.7082 units long.

Length of BC ===

Same process as above.

Find the vertical distance:

$-4--2=-2$

2 units apart vertically.

Find the horizontal distance:

$-3-3=-6$

6 units apart horizontally.

Use the pythagorean theorem:

$2^2+6^2=c^2\\4+36=c^2\\40=c^2\\c=6.3246$

BC is about 6.3246 units long.

Area ===

Finally, you can use these to find the area of the triangle. The area of a right triangle is just half the area of a rectangle with the same base and height:

$A=\frac{b\times h}{2}\\\\A=\frac{6.7082\times6.3246}{2}\\\\A=\frac{42.4264}{2}\\\\A=21.2132$