Which of the equations is graphed below?
Question 1 options:
y = x2 + 6x + 10
y = x2 + 3x + 2
y = x2 - 6x + 10
y = -x2 + 6x - 10
To determine which equation is graphed below, we need to analyze the characteristics of the graph and compare them to the given options.
First, let's observe the general shape of the graph. If the equation is of the form y = ax^2 + bx + c, then the graph will be a parabola.
Next, let's examine the vertex of the parabola. The x-coordinate of the vertex can be found using the formula x = -b / (2a). In this case, the x-coordinate of the vertex is given by x = -b / (2a).
Once we find the x-coordinate of the vertex, we can substitute it into the equation to find the y-coordinate.
Finally, we can evaluate the discriminant, which is b^2 - 4ac, to analyze the concavity of the parabola. If the discriminant is positive, the parabola opens upward. If it is negative, the parabola opens downward.
By analyzing these characteristics for each given option, we can determine which equation matches the graph.