Answer:
Step-by-step explanation:
We can answer this in two ways: Differentiation and Graphing.
<u>Differentitate:</u>
The first derivative of a function yields a function that provides the slope for any point on the line of the original function. The slope of a vertex is zero, so we can set the first derivative to 0 and solve for x.
f(x) = 3(x-1)^2 + 4
f(x) = 3(x-1)(x-1) + 4
f(x) = 3(x^2 - 2x + 1) + 4
f(x) = 3x^2 - 6x + 7
f'(x) = 6x -6
Set this = 0 and find x:
0 = 6x -6
x = 1
The value of y when x=1 in the original equation is:
f(1) = 3(1-1)^2 + 4
y = 4
The vertex is (1,4)
<u>Graph:</u>
You can use DESMOS to plot the function. The result is attached. Look for the vertex and read the coordinates. (1,4) seems to work.
Answer:
A
Step-by-step explanation:
We know that 8+3x= x
solve for x
8= -2x
-4 =x
The only answer that has -4 is A
Answer:
14
Step-by-step explanation:
14
I cant see any statements
Y - x - 3 = 0
y = x + 3
y = x^2 - x - 12
x + 3 = x^2 - x - 12
x^2 - x - 12 - x - 3 = 0
x^2 - 2x - 15 = 0
(x - 5)(x + 3) = 0
x - 5 = 0 y = x + 3
x = 5 y = 5 + 3
y = 8
x + 3 = 0 y = x + 3
x = -3 y = -3 + 3
y = 0
so ur solutions are : (5,8) and (-3,0)