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which statements are true about the graph of the function f(x) = 6x – 4 x2? check all that apply. the vertex form of the functio

Brut [27]

Answer:

The vertex of the function is the point $(-3,-13)$

The graph increase over the interval--------> (-3,∞)

Step-by-step explanation:

we have

$f(x)=6x-4+x^{2}$

1) Convert to vertex form

Group terms that contain the same variable, and move the constant to the opposite side of the equation

$f(x)+4=x^{2}+6x$

Complete the square. Remember to balance the equation by adding the same constants to each side

$f(x)+4+9=x^{2}+6x+9$

$f(x)+13=x^{2}+6x+9$

Rewrite as perfect squares

$f(x)+13=(x+3)^{2}$

$f(x)=(x+3)^{2}-13$ -----> function in vertex form

2) Find the vertex

The vertex of the function is the point $(-3,-13)$

3) Find the axis of symmetry

we know that

In a vertical parabola, the axis of symmetry is equal to the x-coordinate of the vertex

The x-coordinate of the vertex in this problem is equal to $x=-3$

therefore

the equation of the axis of symmetry is $x=-3$

4) Find the increase-decrease intervals

The graph increase over the interval--------> (-3,∞)

The graph decrease over the interval--------> (-∞,-3)

see the attached figure to better understand the problem

5) Find the x-intercepts of the function

we know that

the x-intercepts are the values of x when the value of the function is equal to zero

In this problem the x-intercepts are

$(-6.61,0)$ and $(0.61,0)$

so

The function cross the x-axis twice

see the attached figure

5 0

4 years ago

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The triangles are similar. What is "a" equal to? What is "b" equal to?

TEA [102]

Yes they are if that helps, if you still are unsure than just mesure them and you will see

5 0

3 years ago

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The dress is on sale for 35% off the regular price (w). What expression represents the sale price of the wedding dress?

Aleonysh [2.5K]

Expression that represents the sale price of the wedding dress is $s = 0.65w$

Solution:

Given that, the dress is on sale for 35 % off the regular price

Let the regular price of dress be "w"

To find: Expression that represents the sale price of the wedding dress

Let "s" be the sale price of wedding dress

Sale price = Regular price - discount price

Discount price is given as:

Discount price = 35 % of regular price

Discount price = 35 % of w

$\rightarrow 35 \% \times w\\\\\rightarrow \frac{35}{100} \times w\\\\\rightarrow 0.35w$

Thus discount price = 0.35w

Expression for the sale price of the wedding dress:

Sale price = Regular price - discount price

s = w - 0.35w

s = 0.65w

Thus expression that represents the sale price of the wedding dress is $s = 0.65w$

5 0

3 years ago

Find the area of this trapezoid. Be sure to include the correct unit in your answer. Continue 13 cm 20 cm 8 cm 5 cm 0 0/0 08 cm

kodGreya [7K]

Given:

• Upper Base of trapezoid = 8 cm

,

• Lower base = 20 cm

,

• Length of one leg (also height) = 5 cm

,

• Length of other leg = 13 cm

Let's find the area of the trapezoid.

To find the area of the trapezoid, apply the formula:

$A=\frac{a+b}{2}*h$

Where:

A is the area

a is the length of upper base = 8 cm

b is the length of the lower base = 20 cm

h is the height = 5 cm

Plug in the values for a, b, and h to find the area, A:

$\begin{gathered} A=\frac{8+20}{2}*5 \\ \\ A=\frac{28}{2}*5 \\ \\ A=14*5 \\ \\ A=70\text{ cm}^2 \end{gathered}$

Therefore, the area of the trapezoid is 70 cm^2

8 0

1 year ago

Multiply and simplify (3-5i)(-2+4i)

tia_tia [17]

Answer:

i need answers

Step-by-step explanation:

from any one\

7 0

3 years ago

Read 2 more answers