f(x)=7(x–4)2+3.

3 answers

To find the vertex form of the quadratic function f(x) = 7(x-4)^2 + 3, we need to expand the square:

f(x) = 7(x^2 - 8x + 16) + 3

Next, distribute the 7:

f(x) = 7x^2 - 56x + 112 + 3

Simplify:

f(x) = 7x^2 - 56x + 115

Therefore, the quadratic function f(x) = 7(x-4)^2 + 3 is equivalent to the standard form f(x) = 7x^2 - 56x + 115.
The price of an item was lowered by 25%. By what percent must this discounted price be increased to go back to original price?
responses

25%

30%

33%

40%
To go back to the original price after a 25% discount, we need to increase the discounted price by a certain percentage.

Let's say the original price is x. After a 25% discount, the price becomes 0.75x (since 0.75 is 100% - 25%).

To find the percentage increase to go back to the original price, we need to calculate the difference between the original price and the discounted price, and then express that difference as a percentage of the discounted price.

Difference = x - 0.75x = 0.25x

To find the percentage increase, we divide the difference by the discounted price and multiply by 100:

Percentage increase = (0.25x / 0.75x) * 100 = (1/3) * 100 = 33.33...

Therefore, the discounted price must be increased by approximately 33.33% to go back to the original price. So the correct answer is 33%.