1answer.
Ask question
Login Signup
Ask question
All categories
  • English
  • Mathematics
  • Social Studies
  • Business
  • History
  • Health
  • Geography
  • Biology
  • Physics
  • Chemistry
  • Computers and Technology
  • Arts
  • World Languages
  • Spanish
  • French
  • German
  • Advanced Placement (AP)
  • SAT
  • Medicine
  • Law
  • Engineering
slavikrds [6]
2 years ago
15

What are the exact steps to solve for the x-intercepts of f(x)= −4x2 + 4x + 8? What about −9 = x2 + 6x? Please explain thoroughl

y
Mathematics
1 answer:
victus00 [196]2 years ago
3 0

Answer:

x-intercepts:  (-1, 0) and (2, 0)

x-intercept:  (-3, 0)

Step-by-step explanation:

Given <u>quadratic function</u>:

f(x)=-4x^2+4x+8

The <u>x-intercepts</u> of a <u>quadratic function</u> are the points at which the curve <u>crosses the x-axis</u> ⇒ when y = 0

Therefore, to find the x-intercepts of the given function, set the function to zero:

\implies -4x^2+4x+8=0

Factor out -4:

\implies -4(x^2-x-2)=0

Divide both sides by -4

\implies x^2-x-2=0

Rewrite the middle term as -2x + x:

\implies x^2-2x+x-2=0

Factor the first two terms and the last two terms separately:

\implies x(x-2)+1(x-2)=0

Factor out the common term (x - 2):

\implies (x+1)(x-2)=0

<u>Zero Product Property</u>:  If a ⋅ b = 0 then either a = 0 or b = 0 (or both).

Using the <u>Zero Product Property</u>, set each factor equal to zero and solve for x (if possible):

\begin{aligned}(x+1) & = 0 & \quad \textsf{ or } \quad \quad (x-2) & = 0\\\implies x & = -1 & \implies x & = 2\end{aligned}

Therefore, the x-intercepts are (-1, 0) and (2, 0).

---------------------------------------------------------------------------------------

Given <u>quadratic equation</u>:

-9 = x^2 + 6x

Add 9 to both sides:

\implies x^2+6x+9=0

Rewrite the middle term as 3x + 3x:

\implies x^2+3x+3x+9

Factor the first two terms and the last two terms separately:

\implies x(x+3)+3(x+3)=0

Factor out the common term (x + 3):

\implies (x+3)(x+3)=0

\implies (x+3)^2=0

Square root both sides:

\implies (x+3)=0

Solve for x:

\implies x=-3

Therefore, the x-intercept is (-3, 0).

As the function has a <u>repeated factor</u> (multiplicity of two), the curve will touch the x-axis at (-3, 0) and bounce off.  

You might be interested in
Help Review of linear pair vertical and complementary
Lera25 [3.4K]

Answer:

x = 15

Step-by-step explanation:

The two angles form a straight line so they add to 180 degrees

3+6x   + 5x+12 = 180

Combine like terms

11x+15 = 180

Subtract 15 from each side

11x+15-15 =180-15

11x = 165

Divide by 11

11x/11 =165/11

x =15

7 0
3 years ago
SOMEONE PLEASE HELP ME BEFORE I FAIL
Viefleur [7K]

Answer:

4/40

Step-by-step explanation:

you can reduce this to 1/10

multiplying 4 by both 1 and 10 will give you the fraction 4/40 both can be divided by 4 and that's how it can reduce to the 1st fraction (1/10)

8 0
3 years ago
Choose the graphic representation of the quadratic function f(x)=x^2-8x+24
grigory [225]
The Answer is ----D----

8 0
3 years ago
Read 2 more answers
Y+47x12.6 rewrite the equation below as a function of x
ella [17]
I'm confused is the x a × symbol or the letter x?
3 0
3 years ago
You are constructing a concrete landing pad for a helicopter. You have 4704 cubic feet of concrete.
MAVERICK [17]

a) We have to calculate the height of the pad.

We know that the volume will be 4704 cubic feet.

We also know that the base of the pad is a square of side length 56 feet.

As the volume is the area of the base times the height, we can find the height by dividing the volume by the base area:

\begin{gathered} V=A_b\cdot h \\ h=\frac{V}{A_b}=\frac{4704\text{ ft}^3}{(56\text{ ft})^2}=\frac{4704}{3136}\text{ ft}=1.5\text{ ft} \end{gathered}

The height is 1.5 feet.

b) Now, we have a circular pad of which we know the height (1.5 feet) and the volume (4705 ft³). The area of the base will have to be the same as the are of the square: 3136 ft².

The area of this circular pad can be expressed as πD²/4, so we can calculate the diameter D as:

\begin{gathered} A=3136 \\ \frac{\pi D^2}{4} \\ D^2=3136*\frac{4}{\pi} \\ D^2=3136*\frac{4}{3.14} \\ D^2=3994.9045 \\ D=\sqrt{3994.9045} \\ D\approx63.21 \end{gathered}

The diameter is approximately 63.21 feet.

Answer:

a) The pad will be 1.5 feet thick

b) The diameter will be 63.21 feet.

3 0
1 year ago
Other questions:
  • A family took a trip. They spent $90.71 for gasoline, $153.00 on meals, $197.00 on amusements, and $73.38 on miscellaneous expen
    12·2 answers
  • Sarah spent 1/3 of her monthly budget on food and 3/4 of her monthly budget on gasoline. Sarah has gone over budget and has spen
    13·1 answer
  • Which situation could the expression -255 represent?
    14·1 answer
  • What are the solutions to the equation?
    8·2 answers
  • Solve 9^x + 4 = 11 for x using the change of base formula log base b of y equals log y over log b.
    15·1 answer
  • Did I get this correct
    5·1 answer
  • Select the correct answer.
    7·2 answers
  • Renae and her family are on vacation. During the drive from Denver to Rocky Mountain National Park, she saw 48 travel trailers a
    5·2 answers
  • How r u so good at this
    5·2 answers
  • -5 1/3 converted to an improper fraction
    11·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!