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3 years ago

What is the equation of the axis of symmetry do the quadratic function f(x) = -(x+4) (x-1)

Mathematics

1 answer:

miv72 [106K]3 years ago

8 0

9514 1404 393

Answer:

x = -3/2

Step-by-step explanation:

The zeros of the function are the values of x that make the factors zero:

x = -4, x = 1

The axis of symmetry is the vertical line halfway between these zeros.

x = (-4 +1)/2 = -3/2

The equation of the axis of symmetry is x = -3/2.

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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

Find the cost of 20 grams of lead at 60$ per kilogram

ASHA 777 [7]

Answer:

$1.20

Step-by-step explanation:

Ratio:

Grams : Kilograms

1 : .001

Multiply both sides by 20 to convert grams to kilograms:

Grams : Kilograms

1 : .001

x20 x20

20 : .02

This means that 20 grams of lead = .02 kilograms of lead

Price:

Cost : Kilogram

$60 : 1

Multiply both sides by .02 to find the price of the lead:

Cost : Kilogram

$60 : 1

x.02 x.02

$1.20 : .02

Therefore, .02 kg of lead costs $1.20.

6 0

2 years ago

A.645,473 B.2,151,575 C.8,175,987 D.10,542,719

ELEN [110]

21515754 people total* 0.38= 8175986.52 people

Final answer: C

3 0

3 years ago

Solve the system of equations -2x+y=5 x-3y=-30

EastWind [94]

-2x+y=5
x-3y=-30 so you can multiply the bottom equation by 2 you'll get 2x-6y=-60

-2x+y=5
2x-6y=-60 And subtract the equations. You'll get -5y=-55 y=11. Plug it in to one of the original equations. -2x+(11)=5
-2x=-6 so x=3

y=11 and x=3

5 0

2 years ago

Give the slope and the y-intercept of the line y=9x+7 . Make sure the y-intercept is written as a coordinate.

nekit [7.7K]

Answer:

The slope is 9

The y intercept is (0,7)

Step-by-step explanation:

y=9x+7

The equation is written in slope intercept form

y = mx+b where m is the slope and b is the y intercept

The slope is 9

The y intercept is (0,7)

7 0

2 years ago

What is the equation of the axis of symmetry do the quadratic function f(x) = -(x+4) (x-1)​

What is the equation of the axis of symmetry do the quadratic function f(x) = -(x+4) (x-1)