Algebra 1, Please Help!

Question

Find the vertex of y = -2(x-4)² + 3 and identify it as a minimum or a maximum.

Answer 1

In order to determine if a function has a maximum or a minimum, we must first look if the function is positive or negative. From the function given, -2(x-4)² + 3, we can see the function is negative.

Negative functions will be facing down since they are always decreasing, meaning the vertex will be a maximum point.

To determine the maximum, we can use the formula -b/(2a).

I expanded (x-4)² to get x²-8x+16

from here, the function now looks like this:

-2(x² - 8x + 16) + 3

we then distribute the -2

–2x² + 16 x - 32 + 3

combine like terms

-2x² + 16x -29

will then use the formula ax²+bx+c to determine the value of a and b

a = -2

b = 16

substitute into -b/(2a)

-16/(2*-2) => -16/-4 => 4

substitute 4 into your original equation

Y= -2(4-4)² + 3

when you solve this equation you get 3

The vertex will be at (4,3) and will be the maximum point.

Hope this helps!

Answer 2