Answer for this one please

Could someone help me rnnn?

GuDViN [60]

Answer:

vertex = (0, -4)

equation of the parabola: $y=3x^2-4$

Step-by-step explanation:

Given:

y-intercept of parabola: -4
parabola passes through points: (-2, 8) and (1, -1)

Vertex form of a parabola: $y=a(x-h)^2+k$

(where (h, k) is the vertex and $a$ is some constant)

Substitute point (0, -4) into the equation:

$\begin{aligned}\textsf{At}\:(0,-4) \implies a(0-h)^2+k &=-4\\ah^2+k &=-4\end{aligned}$

Substitute point (-2, 8) and $ah^2+k=-4$ into the equation:

$\begin{aligned}\textsf{At}\:(-2,8) \implies a(-2-h)^2+k &=8\\a(4+4h+h^2)+k &=8\\4a+4ah+ah^2+k &=8\\\implies 4a+4ah-4&=8\\4a(1+h)&=12\\a(1+h)&=3\end{aligned}$

Substitute point (1, -1) and $ah^2+k=-4$ into the equation:

$\begin{aligned}\textsf{At}\:(1.-1) \implies a(1-h)^2+k &=-1\\a(1-2h+h^2)+k &=-1\\a-2ah+ah^2+k &=-1\\\implies a-2ah-4&=-1\\a(1-2h)&=3\end{aligned}$

Equate to find h:

$\begin{aligned}\implies a(1+h) &=a(1-2h)\\1+h &=1-2h\\3h &=0\\h &=0\end{aligned}$

Substitute found value of h into one of the equations to find a:

$\begin{aligned}\implies a(1+0) &=3\\a &=3\end{aligned}$

Substitute found values of h and a to find k:

$\begin{aligned}\implies ah^2+k&=-4\\(3)(0)^2+k &=-4\\k &=-4\end{aligned}$

Therefore, the equation of the parabola in vertex form is:

$\implies y=3(x-0)^2-4=3x^2-4$

So the vertex of the parabola is (0, -4)

5 0

3 years ago

Read 2 more answers

Find x and y<br> Show all the work

vlada-n [284]

Answer:

x = 16

y = 116

Step-by-step explanation:

Given is a figure of isosceles trapezoid. One pair of opposite sides are parallel and non-parallel sides acts as it's transversals.

Therefore,

4x° + (6x + 20)° = 180° ( interior angles on the same side of transversal)

(6x + 20 + 4x)° = 180°

(10x + 20)° = 180°

10x + 20 = 180

10x = 180 - 20

10x = 160

x = 160/10

x = 16

Measure of base angles of an isosceles trapezoid are equal.

Therefore,

y° = (6x + 20)°

y = 6x + 20

y = 6*16 + 20

y = 96 + 20

y = 116

6 0

3 years ago

Use the following function rule to find f(5).<br> f(x) = 2x<br> f(5) =<br> Submit

nikitadnepr [17]

Step-by-step explanation:

f(5) = 2(5) = 10

hope this helps

8 0

3 years ago

The population of bacteria in an

horsena [70]

Answer:

5

Step-by-step explanation:

5 makes sense since the period of time this takes place is 5 days. therefore [?] should be 5

3 0

3 years ago

Read 2 more answers

Me williams asked her students to record a three digit number on thier worksheet bill worte down the number 999 now bill write t

Helga [31]

Answer:

9 hundreds

9 tens

9 ones

Step-by-step explanation:

in math, every digit in a number has a place value.

Place value can be defined as the value represented by a digit in a number on the basis of its position in the number.

The place values to the left of the decimal point are increasing powers of 10:

The first place to the left of the decimal point is the ones place, or 10^0.

The second place to the left of the decimal is the tens place, or 10^1.

The third place to the left of the decimal is the hundreds place, or 10^2.

3 0

3 years ago