All categories

3 years ago

Determine the vertex by completing the square. Show process. y = x2 -6x + 22

Mathematics

1 answer:

Vilka [71]3 years ago

8 0

Answer:

(3,13)

Step-by-step explanation:

$y=x^2-6x+22\\y=x^2-6x+22+3^2-3^2\\y=(x-3)^2+22-9\\y=(x-3)^2+13$

Note that by vertex form we have:

$y=a(x-h)^2+k$

Where the vertex has the coordinates (h,k) so we change the sign of h and keep the same k value and so:

h=3 and k=13

Therefore the vertex of this parabola is: (3,13)

You might be interested in

Find x. A. 11√6/2 B. 22 C. 33 D. 11√3/2

Phoenix [80]

Answer:

Step-by-step explanation:

using the tangent ratio on the triangle on the right and the exact value

tan60° = $\sqrt{3}$ , then letting the altitude be h

tan60° = $\frac{opposite}{adjacent}$ = $\frac{11\sqrt{6} }{h}$ = $\sqrt{3}$ ( multiply both sides by h )

11 $\sqrt{6}$ = h × $\sqrt{3}$ ( divide both sides by $\sqrt{3}$ )

11 $\sqrt{2}$ = h

using the sine ratio in the triangle on the left and the exact value

sin45° = $\frac{\sqrt{2} }{2}$ , then

sin45° = $\frac{opposite}{hypotenuse}$ = $\frac{h}{x}$ = $\frac{11\sqrt{2} }{x}$ = $\frac{\sqrt{2} }{2}$ ( cross- multiply )

$\sqrt{2}$ × x = 22 $\sqrt{2}$ ( divide both sides by $\sqrt{2}$ )

x = 22

6 0

1 year ago

Sally gets paid $15.00 dollars per hour for a 40-hour work week and y dollars for each hour she works over 40 hours. What is the

Anna35 [415]

The equation x = 600 + 8y represents the earnings of Sally if she works 48 hours.

<u>Step-by-step explanation:</u>

Sally gets paid $15.00 dollars per hour for a 40-hour weekly work.
She gets y dollars for each extra hour she works over 40 hours.

<u>The equation can be framed as :</u>

Let,

x be the total pay she could get for 48 hours.
The amount she earned for 40 hours = 40 × $15 ⇒ $600
The amount she earned for extra hours = 8 × y ⇒ 8y

The equation is given as,

Total earnings = amount earned for 40 hours + amount for extra 8 hours.

⇒ x = 600 + 8y

Therefore, the equation x = 600 + 8y represents the earnings of Sally if she works 48 hours.

4 0

3 years ago

The deli server put 0.25 pound (lb) of meat on each sandwich. She used the equation 0.25s = 50 to determine the number of sandwi

LenKa [72]

200 is the value of s

6 0

3 years ago

10(x+12)=15x solve for x with how ?

ankoles [38]

Answer:

x = 24

Step-by-step explanation:

10(x+12)=15x (Given)

10x + 120 = 15x (Distributive property of equality)

-5x = -120 (Subtraction property of equality)

x = 24 (Division property of equality)

7 0

3 years ago

Read 2 more answers

Part of the graph of the function f(x) = (x – 1)(x + 7) is shown below.Which statements about the function are true? Select thre

sertanlavr [38]

The statements about the function that are true are

The vertex of the function is at (–3,–16).
The graph is increasing on the interval x > –3.
The graph is positive only on the intervals where x < –7 and where x > 1.

<h3>How to interpret the graph?</h3>

The equation of the graph is given as

f(x) = (x - 1)(x + 7)

The graph of the function is added as an attachment

On the graph, we have

Vertex = (-3, -16)

This is so because the graph has a minimum point of (-3, -16)

Also, the graph crosses the x-axis at x = 1 and x = -7

This means that the graph is positive at x >1 and x >-7

Because the vertex is a minimum, the graph is increasing at the left of its symmetry i.e. x > -3

Read more about quadratic functions at

brainly.com/question/14933288

#SPJ1

7 0

1 year ago