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Graph f(x) =-2x^+16x-30 by factoring to find the solutions, then find the coordinates of the vertex, and the axis of symmetry. I

fredd [130]

Answer:

Observe attached image

Function zeros:

(3, 0), (5, 0)

Vertex:

(4, 2)

Axis of symmetry:

 $x =4$ 

Step-by-step explanation:

First factorize the function

$f (x) = -2x ^ 2 + 16x-30$

Take -2 as a common factor.

$-2(x ^ 2 -8x +15)$

Now factor the expression $x ^ 2 -8x +15$

You must find two numbers that when you add them, obtain the result -8 and multiplying those numbers results in 15.

These numbers are -5 and -3

Then we can factor the expression in the following way:

$f (x) = -2(x-5)(x-3)$

The quadratic function cuts the x-axis at x = 3 and at x = 5.

Now we find the coordinates of the vertex.

For a function of the form $ax ^ 2 + bx + c$ the x coordinate of its vertex is:

$x = \frac{-b}{2a}$

In the function $f (x) = -2x ^ 2 + 16x-30$

$a = -2\\b = 16\\c = 30$

Then the vertice is:

$x = \frac{-16}{2(-2)}\\\\x = 4$

The y coordinate of the symmetry axis is

$y = f (4) = -2 (4) ^ 2 +16 (4) -30\\\\y = 2$

The axis of symmetry is a vertical line that cuts the parabola in two equal halves. This axis of symmetry always passes through the vertex.

Then the axis of symmetry is the line

$x = 4$

The solutions and the vertice written as ordered pairs are:

Function zeros:

(3, 0), (5, 0)

Vertex:

(4, 2)

6 0

3 years ago

The angle of depression from the top of a lighthouse to a boat is 27*. if the direct distance from the top of lighthouse to the

alisha [4.7K]

Answer:

Correct answer: Db = 411 .18 ft

Step-by-step explanation:

Given:

α = 27° angle of depression

Dt = 462 ft distance from the top of lighthouse to the boat

Db = ? distance from the base of the lighthouse to the boat

Here we have a right triangle with hypotenuse Dt and one leg Db.

By definition

cos α = Db / Dt ⇒ Db = Dt · cos α

Db = 462 · cos 27° = 462 · 0.89 = 411 .18 ft

Db = 411 .18 ft

God is with you!!!

5 0

3 years ago

What is the equation of the following line?

Irina18 [472]

Answer:

Y=5x

Step-by-step explanation:

slope equation

y-y1

x-x1

10-0=10

2-0=2

10/2=5

7 0

2 years ago

A juice shop uses 1/2 of a bag of oranges to make 5 glasses of orange juice. What fraction of a bag of oranges did the shop use

pashok25 [27]

Answer: 0.1 OR 1/10

Step-by-step explanation:

Think about it: There's 1/2 bag of oranges, and you wanna know what number of oranges used in the juice. Take 1/2, and divided it by 5. You get 0.1, then you should turn it into a fraction, giving you 1/10.

6 0

3 years ago

Cameron bought a packet of 45 bars of chocolate.He ate one fifth of them on Tuesday.He ate a twelfth of the remaining bars on We

Vlad1618 [11]

He bought 45 bars of chocolate.

1/5 x 45 = 9
He ate 9 bars on Tuesday.

45 - 9 = 36
He had 36 bars left.

1/12 x 36 = 3
He ate 3 bars on Wednesday

36 - 3 = 33
He had 33 bars left.

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Answer: He had 33 bars left.
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6 0

3 years ago

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