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2 answers:
The vertex form is
where a is the coefficient, and (h,k) is the vertex. Looking at the graph, we see that the vertex is (-2,2), so h is -2 and k is 2. We see that the parabola opens upwards, so A is positive, and is stretched by a factor of 3. (We can find this by looking where the (1,1) should be. We go over 1 from the parabola, and see where the y coordinate is. This is at (-1,5), or 1 unit right and 3 units up.) Therefore, our a is 3. Plugging this into the vertex form:
Which is answer A
where a is the coefficient, and (h,k) is the vertex. Looking at the graph, we see that the vertex is (-2,2), so h is -2 and k is 2. We see that the parabola opens upwards, so A is positive, and is stretched by a factor of 3. (We can find this by looking where the (1,1) should be. We go over 1 from the parabola, and see where the y coordinate is. This is at (-1,5), or 1 unit right and 3 units up.) Therefore, our a is 3. Plugging this into the vertex form:
Which is answer A
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Answer:
-1/5
Step-by-step explanation:
What are parallel lines?
Lines that are parallel never touch. They can extend infinitely and they will still never touch. In order for this to happen the slope of the two lines must be the same. So if we want to find the slope of every line that is parallel to the line on the graph, we simply find the slope of the line of the graph.
Finding the slope
We can find the slope using the following formula:
Where the x and y values are derived from any given points on the line (x1,y1) and (x2,y2)
Here the given points are (-5,-1) and (0,-2)
So we have (x1,y1) = (-5,-1) meaning x1 = -5 and y1 = -1
We also have (x2,y2) = (0,-2) meaning x2 = 0 and y2 = -2
Now we plug these values into the formula
Recall formula :
==> Plug in x1 = -5 , y1 = -1 , x2 = 0 and y2 = -2
==> simplify numerator and denominator
So the slope of the line is -1/5
This means the slope of any parallel line to that line would also have a slope of -1/5