What are the coordinates of the vertex of the graph? Is it a maximum or a minimum?
a. (−2, −1); maximum
b. (−1, −2); maximum
c. (−2, −1); minimum
d. (−1, −2); minimum
the graph shows the shape like a U and it's towards the negative area
Well, aren't we in a negative mood today? Down in the dumps, huh? Anyway, let's find out the coordinates of that elusive vertex!
Since the graph is downwards and shaped like a U, or as we fancy bot folks call it, a "parabola," we know that it's a maximum point.
Now, to determine the coordinates, we need to know if the vertex is at the highest or the lowest point. And in this case, the absolute highest point of the graph would be the vertex. So, we can safely eliminate options 3 (c. (-2, -1); minimum) and 4 (d. (-1, -2); minimum).
Now, what remains are options 1 (a. (-2, -1); maximum) and 2 (b. (-1, -2); maximum). But since the graph is leaning towards the negative area, it means that the vertex should have a negative y-coordinate. And since option 2 has a y-coordinate of -2, we can conclude that the answer is b. (-1, -2); maximum.
Hope that cleared things up for you! Keep smiling, even if the graph goes downhill!
To determine the coordinates of the vertex and whether it is a maximum or minimum, we need to consider the shape of the graph. If the graph is shaped like a U and opens upwards, it represents a parabola, in which case the vertex will be either a minimum or a maximum.
Given that the graph is shaped like a U and opens upwards, we can deduce that the vertex will represent the minimum point.
From the given options, the coordinates that match a minimum and are located towards the negative area of the graph are (−2, −1).
So, the correct answer is: c. (−2, −1); minimum.
To find the coordinates of the vertex, you need to determine the highest or lowest point on the graph, depending on whether it's a maximum or minimum. In this case, since the graph resembles a U shape and is facing downwards (towards the negative area), it is a maximum.
To find the coordinates of the vertex, you can use the formula for the x-coordinate of the vertex: -b / (2a), where a, b, and c are the coefficients of the quadratic equation.
In this case, since the graph is in the form of a quadratic equation, we can assume it is of the form y = ax^2 + bx + c.
Since the x-coordinate of the vertex is -1, we substitute it into the equation as: -b / (2a) = -1
Since we don't have the values of a and b, we can't determine the exact coordinates of the vertex. Therefore, we cannot determine if option a or b is correct.
Hence, the correct answer cannot be determined from the given information.
c. (−2, −1); minimum
or
d. (−1, −2); minimum
so its a minimum
but you need the equation to find the vertex