what would the graph of y=x^2+1 look like
A. a straight line
B. a parabola
C. a dotted line
D. none of the above
The graph of a quadratic function is a parabola.
If you want to see graph
In google type: functions graphs online
When you see list of results click on:
rechneronline.de/function-graphs
When page be open in blue recatacangle type:
x ^ 2 + 1
Then click option Draw
The graph of the equation y = x^2 + 1 would look like a parabola.
To understand why, let's break it down:
1. The equation represents a polynomial function of degree 2 because of the x^2 term.
2. The general form of a quadratic function is y = ax^2 + bx + c, where a, b, and c are constants. In this case, a = 1, b = 0, and c = 1.
3. The coefficient 'a' controls the shape of the parabola. Since a = 1, it means that the parabola opens upward, which is the typical shape of a quadratic equation with a positive leading coefficient.
4. The +1 in the equation shifts the entire parabola one unit up vertically compared to the standard parabola y = x^2.
Based on this analysis, we can conclude that the graph will be a parabola. Thus, the correct answer is B. a parabola.