To sketch: The graph of equation .
The given equation is .
Substitute different values of x to get corresponding values of y in above equation and make a table,
Plot points from above table and connect them by a smooth curve which is shown in Figure (1),
Figure (1) shows the graph of equation that is a parabola.
To find: The x-intercepts and y-intercepts of graph of the equation .
The values of x-intercepts are , 2 and value of y-intercept is .
The equation is,
Substitute 0 for y in equation (1) and solve for x to get the value of x-intercept,
The x-intercept is and 2.
Substitute 0 for x in given equation and solve for y to get the value of y-intercept,
The y-intercept is .
The graph intersects the x-axis at , and these values of x-coordinates called as x-intercepts of graph and the graph intersect y-axis at called as y-intercept of graph shown in above Figure (1).
Thus, the values of x-intercepts are , 2 and value of y-intercept is .
To check: The symmetry of graph of the equation .
The graph of the equation is symmetry about y-axis.
The given equation is,
Replace y by in equation (1) to get new equation,
The above equation is not equivalent to equation (1) so the graph is not symmetric about the x-axis.
Replace x by in the equation (1) to get the new equation,
The above equation is equivalent to equation (1) so the graph is symmetric about y-axis shown in Figure (1),
The Figure (1) shows that the part of the graph to the left of the y-axis is the mirror image of the part to the right of the y-axis and the points , are reflections of each other about the y-axis.
Thus, the graph of the equation is symmetry about y-axis.
Subscribe to bartleby learn! Ask subject matter experts 30 homework questions each month. Plus, you’ll have access to millions of step-by-step textbook answers!