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:
OD) 4.9 units, 14.2 units
<em> The lengths of the legs of a right triangle</em>
<em> </em>a = 4.9units , b = 14.2units and hypotenuse 'c' = 15
Step-by-step explanation:
<u><em>Step(i):-</em></u>
Given that the Acute angle is 19°
And hypotenuse (AC ) = c= 15
We will take cos∝ =
⇒
⇒ BC = 15 × cos 19°
⇒ BC = 15 ×0.9455
⇒ BC = 14.18
The length of the one leg of the right angle triangle
BC = b = 14.18≅ 14.2
We know that ΔABC is a right angle triangle
a² = c² - b²
= 15² - (14.18)²
= 225 - 201.07
= 23.93
a² = 23.93
a = √23.93 = 4.89≅4.9
<u><em>Final answer:-</em></u>
<em> The lengths of the legs of a right triangle</em>
<em> </em>a = 4.9units , b = 14.2units and hypotenuse 'c' = 15
Answer:
B
Step-by-step explanation:
The level of the river is 34 feet, so that is the constant. It drops at a rate of .5 feet per day. This means that the water level is getting lower, so we would be subtracting in this case.