What is y= (x+2) ^2 vertex, axis of symmetry, direction of opening, max or min and y intercept
1 answer:
Answer:
Vertex: (-2, 0)
Axis of symmetry: x = -2
Direction of opening: Upwards
Min: 0
Y-intercept: 4
Step-by-step explanation:
Let us graph this line, and then pull out the details we need. <em>See attached</em>.
What do all of these different things mean?
<u>Vertex:</u> This is where the graph intercepts the axis of symmetry (x = -2, see below) and is at point (-2, 0) for this graph.
<u>Axis of Symmetry:</u> This is the line that the graph is symmetrical across. The "center" of the graph. Here, it is x = -2.
<u>Direction of Opening:</u> The direction that the graph is going/opening towards. In this case, it is upwards.
<u>Min:</u> The minimum (in this case) value, the lowest y-coordinate. This is 0 here.
<u>Y-intercept:</u> The point at which the line intercepts the y-axis. This is 4 here.
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Answer:
36
Step-by-step explanation:
Let's let n be any number.
If we multiply n by 2, we get 2n. Since anything multiplied by 2 is even, 2n <em>must</em> be even. Therefore, let 2n be our first number.
So, the consecutive even number will be (2n+2) followed by (2n+4).
We know that their sum must be 114. Therefore, we can write the following equation:
Solve for n. Combine like terms on the left:
Subtract 6 from both sides:
Finally, divide both sides by 6. Therefore, the value of n is:
Therefore, our first even number is 2n or 2(18) which equates to 36.
And the consecutive even numbers will be 38 and 40.
So, the smallest of them, the first term, is 36.