Answer:
-2
Step-by-step explanation:
Since it would be immensely helpful to know the equation of this parabola, we need to figure it out before we can continue. We have the work form of a positive upwards-opening parabola as
where a is the leading coefficient that determines the steepness of lack thereof of the parabola, x and y are coordinates of a point on the graph, and h and k are the coordinates of the vertex. We know the vertex: V(-3, -3), and it looks like the graph goes through the point P(-2, -1). Now we will fill in the work form equation and solve for a:
which simplifies a bit to
and
-1 = a(1) - 3. Therefore, a = 2 and our parabola is
Now that know the equation, we can find the value of y when x = -3 (which is already given in the vertex) and the value of y when x = -4. Do this by subbing in the values of x one at a time to find y. When x = -3, y = -3 so the coordinate of that point (aka the vertex) is (-3, -3). When x = -4, y = -1 so the coordinate of that point is (-4, -1). The average rate of change between those 2 points is also the slope of the line between those 2 points, so we will use the slope formula to find it:
And there you have it! I'm very surprised that this question sat unanswered for so very long! I'm sorry I didn't see it earlier!
Answer:
See below:
Step-by-step explanation:
We can use the Pythagorean Theorum to find out the missing side because we have a 90 degree right angle and 2 sides already given to us.
The Pythagorean Theorem states that a^2 + b^2 = c^2
<em>a </em>in this case would be the shortest side,
<em>b </em>in this case would be the 2nd longest side,
<em>c </em>is the hypotenuse.
If we solve this, we get 8!
Cheers!
