Im having a hard time figuring out this problem:
Use the function, y=-(x+1)^2 +2, to answer the following parts.
Find the y-intercept
y=-(0+1)^2 +2
y=-(1)^2 +2
y=-1+2
y=1 is my answer
Find the x-intercept
0=-(x+1)^2 +2
0=-((x^2)+(1^2))+2
0=-x^2 - 1 + 2
sq.rt(x^2)= sq.rt(1)
x=1 is my answer but im not sure about it.
I need help with:
Finding the vertex, increasing interval,and decreasing interval.
Is the vertex (-1,2)
Increasing interval (-2,1)
Decreasing interval(1,-2)
Do the x-intercept =1?
1. y= 1 is correct.
2. Y = -(X+1)^2 + 2 = 0,
-(X+1)^2 = -2,
Divide both sides by -1:
(X+1)^2 = 2,
Take sqrt of both sides:
X+1 = sqrt2 = 1.4142,
X = 1.4142 - 1 = 0.4142. = x-Intercept
3. V(-1,2) is correct.
To find the vertex, increasing interval, and decreasing interval of the function y=-(x+1)^2 +2, you can use the concept of vertex form for quadratic functions.
1. Vertex: The vertex form of a quadratic function is given by y = a(x-h)^2 + k, where (h, k) represents the coordinates of the vertex.
In the given function, y=-(x+1)^2 +2, the coefficient of x^2 is -1, which indicates a downward-opening parabola. The vertex form of the function can be written as y=-(x-(-1))^2 +2.
From this, we can determine that the vertex of the parabola is at the point (-1, 2).
2. Increasing Interval: The increasing interval refers to the range of x-values where the function is increasing. In other words, this is the range of x-values where the function's slope is positive.
Since the coefficient of x^2 is negative (-1 in this case), the parabola is opening downwards. As a result, the function is decreasing for all x-values. Therefore, there is no increasing interval.
3. Decreasing Interval: The decreasing interval refers to the range of x-values where the function is decreasing. In other words, this is the range of x-values where the function's slope is negative.
As mentioned earlier, since the parabola opens downward, the function is decreasing for all x-values. So, the decreasing interval is the entire domain of the function.
To summarize:
- Vertex: (-1, 2)
- Increasing Interval: None
- Decreasing Interval: All real numbers
I hope this helps you understand how to find the vertex, increasing interval, and decreasing interval of a quadratic function. Let me know if you have any further questions!