The table below represents a linear function.

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

victus00 [196]

Answer:

x-intercepts: (-1, 0) and (2, 0)

x-intercept: (-3, 0)

Step-by-step explanation:

Given quadratic function:

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

The x-intercepts of a quadratic function are the points at which the curve crosses the x-axis ⇒ 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):

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

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

Using the Zero Product Property, 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 quadratic equation:

$-9 = x^2 + 6x$

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 repeated factor (multiplicity of two), the curve will touch the x-axis at (-3, 0) and bounce off.

3 0

2 years ago

How is Addy 4+ -4 similar to adding 4+4 how is it different use the words and models to explain

Margarita [4]

4- (+) (-4) is similar to 4+4 by the rule of addition in integers that is if Negative + Negative then Add the number and put the sign of greater number.

<h3>What is integer?</h3>

Zero, a positive natural number, or a negative integer denoted by a minus sign are all examples of integers. The inverse additives of the corresponding positive numbers are the negative numbers. An integer, pronounced "IN-tuh-jer," is a whole number that can be positive, negative, or zero and is not a fraction. Integer examples include: -5, 1, 5, 8, 97, and 3,043. 1.43, 1 3/4, 3.14, and other numbers that are not integers are some examples. Three categories of integers exist: Zero (0) (0) Good integers (Natural numbers) Integer Negatives (Additive inverse of Natural Numbers).

The rules of addition in integers says,

- + - = +

by this,

4-(-4)=8

by concept of addition,

4+4=8

To know more about integer,

brainly.com/question/15276410?referrer=searchResults

#SPJ13

3 0

1 year ago

PLEASE PLEASE HELP AND I NEED YOU TO DO IT FAST BECAUSE I HAVE TO GO SOON

Greeley [361]

The height is modelled by the equation:

$h(t)=-0.2t^2+2t$

Therefore

$\begin{gathered} \text{ } \\ \frac{\text{ dh}}{\text{ dt}}=-0.4t+2 \end{gathered}$

At the maximum height dh/dt = 0:

Hence,

$\begin{gathered} -0.4t+2=0 \\ -0.4t=-2 \\ \text{ Dividing both sides by -0.4} \end{gathered}$ $\begin{gathered} \frac{-0.4t}{-0.4}=\frac{-2}{-0.4} \\ t=5 \end{gathered}$

Hence, the ball gets to the maximum height after 5s.

The maximum height is given by h(5):

$h(5)=-0.2(5)^2+2(5)=5$

Therefore, the maximum height is 5 ft.

When the ball reaches the ground h(t) = 0:

$\begin{gathered} -0.2t^2+2t=0 \\ \text{ Dividing both sides by -0.2, we have:} \\ t^2-10t=0 \\ Factorising\text{ the left hand side, we have} \\ t(t-10)=0 \\ \text{ Therefore,} \\ t=0,\text{ t=10} \end{gathered}$

The ball reaches the ground in 10s

.

8 0

1 year ago

A street has parallel curbs 40 feet apart. A crosswalk bounded by two parallel stripes crosses the street at an angle. The lengt

andreev551 [17]

Answer:

The distance, in feet, between the strip = 12 feet.

Step-by-step explanation:

From the figure attached in relation with the question, we can deduce that crosswalk is a parallelogram where

CD/AB = CE/AE

CD = 40

CE = 50

AE = 15

Let AB = x

50x = 15 × 40

X = 12

The distance, in feet, between the strip is therefore 12 feet

6 0

3 years ago

Is the coldest temperature represented by a positive or negative number? * Positive Negative

dimulka [17.4K]

The coldest temp is negative

6 0

4 years ago