All categories

2 years ago

Rewrite the function by completing the square. f(x)=x^2-4x-26

Mathematics

1 answer:

Radda [10]2 years ago

5 0

Answer:

$(x-2)^2-30$

Step-by-step explanation:

use the form $ax^2+bx+c$ to find the values of a, b, and c.

$a=1, b= -4, c = -26$

consider the vertex form of a parabola

$a(x+d)^2+e$

substitute the values of a and b into the formula $d=\frac{b}{2a}$

$d=\frac{4}{2(1)}$

simplify the right side.

find the value of e using the formula $e=c-\frac{b^2}{4a}$

$e=30$

You might be interested in

LA plane is trying to travel 250 miles at a bearing of 20° E of S, however, it ends 230 miles away from the

Semmy [17]

Answer:

The wind pushed the plane $65.01$ miles in the direction of $45.56 ^{\circ}$ East of North with respect to the destination point.

Step-by-step explanation:

Let origin, O, br the starting point and point D be the destination at 250 miles at a bearing of 20° E of S, but due to wind let D' be the actual position of the plane at 230 miles away from the starting point in the direction of 35° E of South as shown in the figure.

So, we have |OD|=250 miles and |OD'|=230 miles.

Vector $\overrightarrow{DD'}$ is the displacement vector of the plane pushed by the wind.

From figure, the magnitude of the required displacement vector is

$|DD'|=\sqrt{|AB|^2+|PQ|^2}\;\cdots(i)$

and the direction is $\alpha$ east of north as shown in the figure,

$\tan \alpha=\frac{|PQ|}{|AB|}\;\cdots(ii)$

From the figure,

$|AB|=|OA-OB|$

$\Rightarrow |AB|=|OD\cos 20 ^{\circ}-OD'\cos 35 ^{\circ}|$

$\Rightarrow |AB|=|250\cos 20 ^{\circ}-230\cos 35 ^{\circ}|$

$\Rightarrow |AB|=45.52$ miles

Again, $|PQ|=|OP-OQ|$

$\Rightarrow |PQ|=|OD\sin 20 ^{\circ}-OD'\sin 35 ^{\circ}|$

$\Rightarrow |PQ|=|250\sin 20 ^{\circ}-230\sin 35 ^{\circ}|$

$\Rightarrow |PQ|=46.42$ miles

Now, from equations (i) and (ii), we have

$|DD'|=\sqrt{|45.52|^2+|46.42|^2}=65.01$ miles, and

$\tan \alpha=\frac{|46.42|}{|45.52|}$

$\alpha=\tan^{-1}\left(\frac{|46.42|}{|45.52|}\right)=45.56 ^{\circ}$

Hence, the wind pushed the plane $65.01$ miles in the direction of $45.56 ^{\circ}$ E astof North with respect to the destination point.

5 0

3 years ago

A game room has a floor that is 100 feet by 30 feet. A scale drawing of the floor on grid paper uses a scale of 3 units:5 feet.

Ghella [55]

3 units/ 5 feet = 60 units/ 100 feet
3 units/ 5 feet = 18 units/ 30 feet

The dimensions of the scale drawing are 60 units by 18 units.

Hope this helps!

7 0

3 years ago

Need help with my Geometry, can someone help me with 4,5 and 10?

xz_007 [3.2K]

For questions 4 and 5, use laws of complementary and supplementary angles to find values of x. I'm not too sure about what question 10 is asking.

Hope I helped :)