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.
sample response: The pre-image is the point you start with. To check the transformation rule, substitute the values of the coordinates (4, 5) into the rule. You get (4, 5) → (4+4, 5+7). Simplify to get (4, 5) → (8, 12). This is the image. Instead the rule was applied to the image. This is the source of the error.
Answer:
It is b
Step-by-step explanation:
Answer:
z would be at (-6,6)
Step-by-step explanation:
hope that helps