A parabola has x-intercepts at -3 and 4. Write 2 possible equations of parabolas in

Help!! 50 points and brainliest!

Viktor [21]

Answer:

Second choice:

$x=2t$

$y=4t^2+4t-3$

Fifth choice:

$x=t+1$

$y=t^2+4t$

Step-by-step explanation:

Let's look at choice 1.

$x=t+1$

$y=t^2+2t$

I'm going to subtract 1 on both sides for the first equation giving me $x-1=t$ . I will replace the $t$ in the second equation with this substitution from equation 1.

$y=(x-1)^2+2(x-1)$

Expand using the distributive property and the identity $(u+v)^2=u^2+2uv+v^2$ :

$y=(x^2-2x+1)+(2x-2)$

$y=x^2+(-2x+2x)+(1-2)$

$y=x^2+0+-1$

$y=x^2$

So this not the desired result.

Let's look at choice 2.

$x=2t$

$y=4t^2+4t-3$

Solve the first equation for $t$ by dividing both sides by 2:

$t=\frac{x}{2}$ .

Let's plug this into equation 2:

$y=4(\frac{x}{2})^2+4(\frac{x}{2})-3$

$y=4(\frac{x^2}{4})+2x-3$

$y=x^2+2x-3$

This is the desired result.

Choice 3:

$x=t-3$

$y=t^2+2t$

Solve the first equation for $t$ by adding 3 on both sides:

$x+3=t$ .

Plug into second equation:

$y=(x+3)^2+2(x+3)$

Expanding using the distributive property and the earlier identity mentioned to expand the binomial square:

$y=(x^2+6x+9)+(2x+6)$

$y=(x^2)+(6x+2x)+(9+6)$

$y=x^2+8x+15$

Not the desired result.

Choice 4:

$x=t^2$

$y=2t-3$

I'm going to solve the bottom equation for $t$ since I don't want to deal with square roots.

Add 3 on both sides:

$y+3=2t$

Divide both sides by 2:

$\frac{y+3}{2}=t$

Plug into equation 1:

$x=(\frac{y+3}{2})^2$

This is not the desired result because the $y$ variable will be squared now instead of the $x$ variable.

Choice 5:

$x=t+1$

$y=t^2+4t$

Solve the first equation for $t$ by subtracting 1 on both sides:

$x-1=t$ .

Plug into equation 2:

$y=(x-1)^2+4(x-1)$

Distribute and use the binomial square identity used earlier:

$y=(x^2-2x+1)+(4x-4)$

$y=(x^2)+(-2x+4x)+(1-4)$

$y=x^2+2x+-3$

$y=x^2+2x-3$ .

This is the desired result.

3 0

4 years ago

Read 2 more answers

30% of 70 Explain the process to!

Sav [38]

There r 2 ways to do this type of problem....

(1) 30% of 70...turn percent to decimal...." of " means multiply
0.30(70) = 21.....so 30% of 70 is 21

or

(2) use the percent formula.....is/of = %/100
30% of 70 is what ...
is = x
of = 70
% = 30

is/of = %/100
sub
x / 70 = 30 / 100
cross multiply because this is a proportion
(100)(x) = (30)(70)
100x = 2100
x= 2100 / 100
x = 21
** by the way, this percent formula works on many percent problems...u just have to make sure u sub the right numbers in the right places.

either way u choose to do it, u should arrive at the same answer

6 0

3 years ago

Read 2 more answers

How do I do #6?? GEOMETRY

nexus9112 [7]

The two slanted lines BC and AD are the same, then AD should be the same length, 27.

7 0

4 years ago

Please help! The problem is in the picture:

Alja [10]

Answers:

a = 8
r = -15%
y = 4.9 approximately

Note: your teacher may want you to type in a positive value for r

=========================================================

Explanation:

The given equation y = 8(1-0.15)^t is in the form y = a(1+r)^t

We have a = 8 as the initial value, or what we start with.

r = -0.15 converts to -15%, so we have a decay of 15%

Plug in t = 3 to find the corresponding value of y

y = 8(1-0.15)^t

y = 8(1-0.15)^3

y = 8(0.85)^3

y = 8(0.614125)

y = 4.913

y = 4.9

3 0

3 years ago

Read 2 more answers

A donut shop made 12 dozen donuts to give to a school’s math club.

erica [24]

Answer:

Number of donuts each student get = 144 / x

Step-by-step explanation:

Given:

Number of donuts = 12 dozen

Number of students = x

Find:

How many donuts each student get

Computation:

Total number of donuts = 12 × 12 = 144

Number of donuts each student get = Total number of donuts / Number of students

Number of donuts each student get = 144 / x

8 0

4 years ago