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2 years ago

Write the function in standard form f(x) = -4 (x - 6)^2 + 15

Mathematics

2 answers:

amid [387]2 years ago

7 0

9514 1404 393

Answer:

f(x) = -4x^2 +48x -129

Step-by-step explanation:

It usually works well to compute the square first. That is, simplify according to the order of operations.

f(x) = -4(x^2 -12x +36) +15

f(x) = -4x^2 +48x -144 +15

f(x) = -4x^2 +48x -129

Alchen [17]2 years ago

5 0

Answer:

f(x) = -4x² + 48x - 129

Step-by-step explanation:

Given the quadratic function in vertex form, f(x) = -4(x - 6)² + 15:

In order to transform the given function into its standard form, f(x) = ax² + bx + c, expand the squared binomial (without distributing -4 and adding 15).

f(x) = -4(x - 6)² + 15

f(x) = -4(x² - 6x - 6x + 36) + 15

Combine like terms:

f(x) = -4(x² -12x + 36) + 15

Distribute -4 into the parenthesis:

f(x) = -4x² + 48x - 144 + 15

Combine the constants:

f(x) = -4x² + 48x - 129 ⇒ This is the quadratic function in standard form where a = -4, b = 48, and c = -129.

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Find a cartesian equation for the curve. r = 9 sin(θ)

Paul [167]

For this case we have the following equation:
r = 9 sin (θ)
In addition, we have the following change of variables:
y = r * sine (θ)
Rewriting the equation we have:
r = 9 sin (θ)
r = 9 (y / r)
r ^ 2 = 9y
On the other hand:
r ^ 2 = x ^ 2 + y ^ 2
Substituting values:
x ^ 2 + y ^ 2 = 9y
Rewriting:
x ^ 2 + y ^ 2 - 9y = 0
Completing squares:
x ^ 2 + y ^ 2 - 9y + (-9/2) ^ 2 = (-9/2) ^ 2
Rewriting:
x ^ 2 + 1/4 (2y-9) ^ 2 = 81/4
4x ^ 2 + (2y-9) ^ 2 = 81
Answer:
The Cartesian equation is:
4x ^ 2 + (2y-9) ^ 2 = 81

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3 years ago

Find the area of the rectangle. Show your work!

Nesterboy [21]

3x^2 - 7x - 20

use FOILING

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3 years ago

In the graph of an inequality, the region to the right of a dashed vertical line

lara31 [8.8K]

Answer:

x is greater than -4

Step-by-step explanation:

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3 years ago

Nico can do 42 push-ups in 3 minutes.

Alchen [17]

Step-by-step explanation:

Hey there!

It is said we need to find the unit rate.

What we can do is apply Unitary Method.

3 minutes = 42 push ups

1 minute = $\sf{\bf{\dfrac{42}{3}}}$

<u>So, 12 push ups per minute is the unit rate.</u>

In 5 minutes, he will do 12×5 = <u>60 push ups!</u>

Hope it helps :)

4 0

3 years ago

Pls help me .question no 14

Alex_Xolod [135]

Question 14, Part (i)

Focus on quadrilateral ABCD. The interior angles add to 360 (this is true for any quadrilateral), so,

A+B+C+D = 360

A+90+C+90 = 360

A+C+180 = 360

A+C = 360-180

A+C = 180

Since angles A and C add to 180, this shows they are supplementary. This is the same as saying angles 2 and 3 are supplementary.

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

Question 14, Part (ii)

Let

x = measure of angle 1

y = measure of angle 2

z = measure of angle 3

Back in part (i) above, we showed that y + z = 180

Note that angles 1 and 2 are adjacent to form a straight line, so we can say

x+y = 180

-------

We have the two equations x+y = 180 and y+z = 180 to form this system of equations

$\begin{cases}x+y = 180\\y+z = 180\end{cases}$

Which is really the same as this system

$\begin{cases}x+y+0 = 180\\0+y+z = 180\end{cases}$

The 0s help align the y terms up. Subtracting straight down leads to the equation x-z = 0 and we can solve to get x = z. Therefore showing that angle 1 and angle 3 are congruent. We could also use the substitution rule to end up with x = z as well.

4 0

4 years ago