SOLUTION: 1. State the key features listed for the following parabola: f(x)=-0.5(x+1)2-7 Vertex Direction of opening Axis of symmetry min/max value

Question 1198783: 1. State the key features listed for the following parabola: f(x)=-0.5(x+1)2-7

Vertex

Direction of opening

Axis of symmetry

min/max value

range

y-intercept

2. State the domain and range of the following:

a) f(x)=0.5(x+1)2+7
b) f(x)=-3x+4

Answer by math_tutor2020(3816) (Show Source): You can put this solution on YOUR website!

Answers for problem 1 in red
Vertex: (-1, -7)
Direction of opening: downward
Axis of symmetry: x = -1
min/max value: Max is y = -7
range: y ≤ -7
y-intercept: -7.5

Explanation:

Compare y = -0.5(x+1)^2-7 to y = a(x-h)^2+k
We find that h = -1 and k = -7
Think of x+1 as x-(-1)
Therefore, the vertex is (h,k) = (-1, -7)

The value of 'a' determines directly how the parabola opens.
If a < 0, then the parabola opens downward.
If a > 0, then the parabola opens upward.
In this case we have a = -0.5 to indicate the parabola opens downward.

The axis of symmetry is of the form x = h, where h was the x coordinate of the vertex.
The axis of symmetry is the vertical mirror line through the vertex.
Therefore, h = -1 leads to x = -1 being the axis of symmetry.

Recall in the second paragraph we discussed a = -0.5 indicating the parabola opens downward.
This causes the vertex to be the highest point, aka max.
The max value is the largest possible y output which in this case is y = -7.
This is the highest the parabola can go before falling back down.

Refer to the previous paragraph above. We found that y = -7 is the largest output possible.
The range is the set of possible y outputs. Either y = -7 or y < -7.
In short, the range is the set of y values such that

To find the y-intercept, plug in x = 0 and compute.
y = -0.5(x+1)^2 - 7
y = -0.5(0+1)^2 - 7
y = -7.5
The y-intercept is -7.5; placing it at the location (0,-7.5)

Graph:

I recommend using either Desmos or GeoGebra as a graphing tool.
Both of which are free.

I'll leave problem 2 for you to complete.
If you're still stuck, then let me know or make a new post on this website.

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