The equation y = -x^2+6x+5 is really the equation y = -1x^2+6x+5. It is in the form y = ax^2 + bx + c where
a = -1
b = 6
c = 5
We will use 'a' and 'b' in the formula below
h = -b/(2a)
h = -6/(2*(-1))
h = -6/(-2)
h = 3
The h refers to the x coordinate of the vertex. Since we know the x coordinate of the vertex (is 3), we can use it to find the y coordinate of the vertex
Simply plug x = 3 into the original equation
y = -x^2 + 6x + 5
y = -(3)^2 + 6(3) + 5
y = -(9) + 6(3) + 5
y = -9+18+5
y = 14
This is the k value, so k = 14.
In summary so far, we have a = -1, h = 3 and k = 14. Plug all this into the vertex form below
y = a(x-h)^2 + k
y = -1(x-3)^2 + 14
y = -(x-3)^2 + 14
Therefore the vertex form equation is y = -(x-3)^2 + 14
So when x = 3, the paired y value is y = 14. The point (x,y) = (3,14) is a point on the parabola. This point is either the highest or lowest point.
How can we figure out if it's the highest or lowest point? By looking at the value of 'a'. Notice how a = -1 and this is less than zero. In other words, a < 0
Since a < 0, this means the parabola opens downward forming a "frown" so to speak. That's one way to remember it: negative 'a' leads to sad face.
Anyways, this parabola opening downward means that the vertex is the highest point.
So (3,14) is the vertex
The maximum is y = 14.
Answer:
x = 55
Step-by-step explanation:
The "equals" sign means both sides are equal. You want to isolate the x. So subtract 22 from both sides.
62+15-22 = x
62-22 = 40; 40 + 15 = 55
x = 55
Answer:
Graph 3 satisfy the slope condition of speed with Time 6 hours and Distance 15 miles
Step-by-step explanation:
Given as :
The distance of trail is 15 miles
The Rate of hikes = 2.5 mph
So, Time taken = T
Now Time =
Or, Time =
Or, Time = 6 hours
So, The graph Between Distance and Time is
D = Speed × Time
Or, Speed is slope of the function
∴ Graph 3 satisfy the slope condition of speed with Time 6 hours and Distance 15 miles Answer
Answer:
ummmm click on the one u r on
Step-by-step explanation:
Answer:
2
Step-by-step explanation:
64x64=4096
So its 64^2=4096